Question 1

The graph of a quadratic function is given. Determine the function's equation.
-
A) $h ( x ) = ( x - 2 ) ^ { 2 } + 2$
B) $j ( x ) = ( x - 2 ) ^ { 2 } - 2$
C) $g ( x ) = ( x + 2 ) ^ { 2 } - 2$
D) $f ( x ) = ( x + 2 ) ^ { 2 } + 2$

Accepted Answer

A

Question 2

The graph of a quadratic function is given. Determine the function's equation.
-
A) $f ( x ) = ( x + 2 ) ^ { 2 } + 2$
B) $h ( x ) = ( x - 2 ) ^ { 2 } + 2$
C) $g ( x ) = ( x + 2 ) ^ { 2 } - 2$
D) $j ( x ) = ( x - 2 ) ^ { 2 } - 2$

Accepted Answer

D

Question 3

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = x ^ { 2 } + 6$$
A) $( 0,6 )$
B) $( 0 , - 6 )$
C) $( 6,0 )$
D) $( - 6,0 )$

Accepted Answer

The vertex form of a parabola is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For $f(x) = x^2 + 6$, it's already in a form where $h = 0$ and $k = 6$, making the vertex $(0, 6)$.

Question 4

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = 6 - ( x + 4 ) ^ { 2 }$$
A) $( 4,6 )$
B) $( 6 , - 4 )$
C) $( - 4,6 )$
D) $( 6,4 )$

Accepted Answer

The vertex form of a quadratic function is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. The given function can be rewritten as $f(x) = -1(x + 4)^2 + 6$, which matches the vertex form with $h = -4$ and $k = 6$, making the vertex $(-4, 6)$.

Question 5

The graph of a quadratic function is given. Determine the function's equation.
-
A) $j ( x ) = x ^ { 2 } + 3$
B) $f ( x ) = x ^ { 2 } - 6 x + 9$
C) $g ( x ) = x ^ { 2 } + 6 x + 9$
D) $h ( x ) = x ^ { 2 } - 3$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 6

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = x ^ { 2 } - 5$$
A) $( 1,0 )$
B) $( 5,0 )$
C) $( 0 , - 5 )$
D) $( 0,5 )$

Accepted Answer

The vertex form of a parabola is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For the given function $f(x) = x^2 - 5$, it is already in a form where $a = 1$, $h = 0$, and $k = -5$, indicating the vertex is at $(0, -5)$.

Question 7

The graph of a quadratic function is given. Determine the function's equation.
-
A) $f ( x ) = x ^ { 2 } - 4 x + 4$
B) $g ( x ) = x ^ { 2 } + 4 x + 4$
C) $j ( x ) = x ^ { 2 } + 2$
D) $h ( x ) = x ^ { 2 } - 2$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 8

The graph of a quadratic function is given. Determine the function's equation.
-
A) $g ( x ) = - x ^ { 2 } + 4 x + 4$
B) $h ( x ) = - x ^ { 2 } - 2$
C) $j ( x ) = - x ^ { 2 } + 2$
D) $f ( x ) = - x ^ { 2 } - 4 x - 4$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 9

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = ( x + 4 ) ^ { 2 } - 8$$
A) $( - 4 , - 8 )$
B) $( 4 , - 8 )$
C) $( 4,8 )$
D) $( - 4,8 )$

Accepted Answer

The vertex form of a parabola is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. The given equation is already in vertex form with $h = -4$ and $k = -8$, making the vertex $(-4, -8)$.

Question 10

The graph of a quadratic function is given. Determine the function's equation.
-
A) $g ( x ) = x ^ { 2 } + 6 x + 9$
B) $f ( x ) = x ^ { 2 } - 6 x + 9$
C) $j ( x ) = x ^ { 2 } + 3$
D) $h ( x ) = x ^ { 2 } - 3$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 11

The graph of a quadratic function is given. Determine the function's equation.
-
A) $h ( x ) = ( x - 2 ) ^ { 2 } + 2$
B) $f ( x ) = ( x + 2 ) ^ { 2 } + 2$
C) $g ( x ) = ( x + 2 ) ^ { 2 } - 2$
D) $j ( x ) = ( x - 2 ) ^ { 2 } - 2$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 12

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$y + 4 = ( x + 2 ) ^ { 2 }$$
A) $( - 2 , - 4 )$
B) $( 4,2 )$
C) $( 2 , - 4 )$
D) $( 4 , - 2 )$

Accepted Answer

The given equation is in vertex form $y = a(x-h)^2 + k$, where $(h, k)$ is the vertex of the parabola. Comparing, we find $h = -2$ and $k = -4$, so the vertex is $(-2, -4)$.

Question 13

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = x ^ { 2 } - 10 x - 7$$
A) $( 5 , - 32 )$
B) $( - 5,68 )$
C) $( 5 , - 82 )$
D) $( - 10,193 )$

Accepted Answer

The vertex of a parabola defined by $f(x) = ax^2 + bx + c$ can be found using the formula $(-\frac{b}{2a}, f(-\frac{b}{2a}))$. For $f(x) = x^2 - 10x - 7$, $a = 1$, $b = -10$, and $c = -7$. Thus, the x-coordinate of the vertex is $-\frac{-10}{2*1} = 5$. Substituting $x = 5$ into the original equation gives $f(5) = 5^2 - 10*5 - 7 = 25 - 50 - 7 = -32$. Therefore, the vertex is $(5, -32)$.

Question 14

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = ( x + 3 ) ^ { 2 } + 8$$
A) $( 8 , - 9 )$
B) $( - 3,8 )$
C) $( - 8,3 )$
D) $( 8 , - 3 )$

Accepted Answer

The vertex form of a parabola is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. In the given function $f(x) = (x + 3)^2 + 8$, it matches the vertex form with $h = -3$ and $k = 8$, making the vertex $(-3, 8)$.

Question 15

The graph of a quadratic function is given. Determine the function's equation.
-
A) $f ( x ) = - x ^ { 2 } - 4 x - 4$
B) $j ( x ) = - x ^ { 2 } + 2$
C) $g ( x ) = - x ^ { 2 } + 4 x + 4$
D) $h ( x ) = - x ^ { 2 } - 2$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 16

The graph of a quadratic function is given. Determine the function's equation.
-
A) $h ( x ) = x ^ { 2 } - 1$
B) $i ( x ) = x ^ { 2 } + 1$
C) $f ( x ) = x ^ { 2 } - 2 x + 1$
D) $g ( x ) = x ^ { 2 } + 2 x + 1$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 17

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 6$$
A) $( - 2 , - 6 )$
B) $( - 6,2 )$
C) $( 2 , - 6 )$
D) $( - 7 , - 2 )$

Accepted Answer

The vertex form of a parabola is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For the given function $f(x) = -7(x - 2)^2 - 6$, the vertex is $(2, -6)$.

Question 18

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = 11 ( x - 4 ) ^ { 2 } + 5$$
A) $( - 4,5 )$
B) $( 11,4 )$
C) $( 4,5 )$
D) $( 5 , - 4 )$

Accepted Answer

The vertex form of a parabola is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For the given function, $h = 4$ and $k = 5$, making the vertex $(4, 5)$.

Question 19

The graph of a quadratic function is given. Determine the function's equation.
-
A) $h ( x ) = ( x - 1 ) ^ { 2 } + 1$
B) $j ( x ) = ( x - 1 ) ^ { 2 } - 1$
C) $f ( x ) = ( x + 1 ) ^ { 2 } + 1$
D) $g ( x ) = ( x + 1 ) ^ { 2 } - 1$

Accepted Answer

The answer of The graph of a quadratic function is...

Question 20

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = ( x + 5 ) ^ { 2 } + 5$$
A) $( 5,0 )$
B) $( - 5 , - 5 )$
C) $( 0,5 )$
D) $( - 5,5 )$

Accepted Answer

The vertex form of a parabola is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Given $f(x) = (x + 5)^2 + 5$, it matches the vertex form with $h = -5$ and $k = 5$, making the vertex $(-5, 5)$.

Quiz 3: Polynomial and Rational Functions

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 6$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 6 - ( x + 4 ) ^ { 2 }$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) j ( x ) = x ^ { 2 } + 3 B) f ( x ) = x ^ { 2 } - 6 x + 9 C) g ( x ) = x ^ { 2 } + 6 x + 9 D) h ( x ) = x ^ { 2 } - 3$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } - 5$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) f ( x ) = x ^ { 2 } - 4 x + 4 B) g ( x ) = x ^ { 2 } + 4 x + 4 C) j ( x ) = x ^ { 2 } + 2 D) h ( x ) = x ^ { 2 } - 2$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) g ( x ) = - x ^ { 2 } + 4 x + 4 B) h ( x ) = - x ^ { 2 } - 2 C) j ( x ) = - x ^ { 2 } + 2 D) f ( x ) = - x ^ { 2 } - 4 x - 4$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } - 8$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) g ( x ) = x ^ { 2 } + 6 x + 9 B) f ( x ) = x ^ { 2 } - 6 x + 9 C) j ( x ) = x ^ { 2 } + 3 D) h ( x ) = x ^ { 2 } - 3$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $y + 4 = ( x + 2 ) ^ { 2 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } - 10 x - 7$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 3 ) ^ { 2 } + 8$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) f ( x ) = - x ^ { 2 } - 4 x - 4 B) j ( x ) = - x ^ { 2 } + 2 C) g ( x ) = - x ^ { 2 } + 4 x + 4 D) h ( x ) = - x ^ { 2 } - 2$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) h ( x ) = x ^ { 2 } - 1 B) i ( x ) = x ^ { 2 } + 1 C) f ( x ) = x ^ { 2 } - 2 x + 1 D) g ( x ) = x ^ { 2 } + 2 x + 1$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 6$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 11 ( x - 4 ) ^ { 2 } + 5$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 5 ) ^ { 2 } + 5$

Quiz 3: Polynomial and Rational Functions

The graph of a quadratic function is given. Determine the function's equation. -

The graph of a quadratic function is given. Determine the function's equation. -

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =x2+6f ( x ) = x ^ { 2 } + 6f(x) =x2+6

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =6−(x+4) 2f ( x ) = 6 - ( x + 4 ) ^ { 2 }f(x) =6−(x+4) 2

The graph of a quadratic function is given. Determine the function's equation. -

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =x2−5f ( x ) = x ^ { 2 } - 5f(x) =x2−5

The graph of a quadratic function is given. Determine the function's equation. -

The graph of a quadratic function is given. Determine the function's equation. -

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =(x+4) 2−8f ( x ) = ( x + 4 ) ^ { 2 } - 8f(x) =(x+4) 2−8

The graph of a quadratic function is given. Determine the function's equation. -

The graph of a quadratic function is given. Determine the function's equation. -

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - y+4=(x+2) 2y + 4 = ( x + 2 ) ^ { 2 }y+4=(x+2) 2

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =x2−10x−7f ( x ) = x ^ { 2 } - 10 x - 7f(x) =x2−10x−7

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =(x+3) 2+8f ( x ) = ( x + 3 ) ^ { 2 } + 8f(x) =(x+3) 2+8

The graph of a quadratic function is given. Determine the function's equation. -

The graph of a quadratic function is given. Determine the function's equation. -

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =−7(x−2) 2−6f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 6f(x) =−7(x−2) 2−6

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =11(x−4) 2+5f ( x ) = 11 ( x - 4 ) ^ { 2 } + 5f(x) =11(x−4) 2+5

The graph of a quadratic function is given. Determine the function's equation. -

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x) =(x+5) 2+5f ( x ) = ( x + 5 ) ^ { 2 } + 5f(x) =(x+5) 2+5

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 6$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 6 - ( x + 4 ) ^ { 2 }$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) j ( x ) = x ^ { 2 } + 3 B) f ( x ) = x ^ { 2 } - 6 x + 9 C) g ( x ) = x ^ { 2 } + 6 x + 9 D) h ( x ) = x ^ { 2 } - 3$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } - 5$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) f ( x ) = x ^ { 2 } - 4 x + 4 B) g ( x ) = x ^ { 2 } + 4 x + 4 C) j ( x ) = x ^ { 2 } + 2 D) h ( x ) = x ^ { 2 } - 2$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) g ( x ) = - x ^ { 2 } + 4 x + 4 B) h ( x ) = - x ^ { 2 } - 2 C) j ( x ) = - x ^ { 2 } + 2 D) f ( x ) = - x ^ { 2 } - 4 x - 4$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } - 8$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) g ( x ) = x ^ { 2 } + 6 x + 9 B) f ( x ) = x ^ { 2 } - 6 x + 9 C) j ( x ) = x ^ { 2 } + 3 D) h ( x ) = x ^ { 2 } - 3$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $y + 4 = ( x + 2 ) ^ { 2 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } - 10 x - 7$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 3 ) ^ { 2 } + 8$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) f ( x ) = - x ^ { 2 } - 4 x - 4 B) j ( x ) = - x ^ { 2 } + 2 C) g ( x ) = - x ^ { 2 } + 4 x + 4 D) h ( x ) = - x ^ { 2 } - 2$

The graph of a quadratic function is given. Determine the function's equation. - $The graph of a quadratic function is given. Determine the function's equation. - A) h ( x ) = x ^ { 2 } - 1 B) i ( x ) = x ^ { 2 } + 1 C) f ( x ) = x ^ { 2 } - 2 x + 1 D) g ( x ) = x ^ { 2 } + 2 x + 1$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 6$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 11 ( x - 4 ) ^ { 2 } + 5$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 5 ) ^ { 2 } + 5$