Deck 3: Quadratic Functions

Question 1

Find the zeros of $Q(r)=2 r-15+r^{2}$ by factoring. List the answers in the form "A, $\mathrm{B}$ ", with $\mathrm{A}<\mathrm{B}$ .

Answer 1

$-5,3$

Question 2

Find the zeros of $y=10 x^{2}+15 x+5$ . List the answers in the form "A, B", with $\mathrm{A}<\mathrm{B}$ .

Answer 2

$-1,-0.5$

Question 3

Which of the following quadratic functions have zeros at $x=-4$ and $x=1$ ?

A) $x^{2}+3 x-4$
B) $x^{2}-3 x-4$
C) $5 x^{2}+15 x-20$
D) $5 x^{2}-15 x-20$

Answer 3

$x^{2}+3 x-4$
$5 x^{2}+15 x-20$

Question 4

Solve $3.2 x^{2}-4.5 x=6.5$ by the quadratic formula. Round your answers to 2 decimal places. List the answers in the form "A, B", with $\mathrm{A}<\mathrm{B}$ .

Question 5

If $p(t)=-4(t-2)(t+1)$ is quadratic, then it can be written as
$p(t)=\ldots t^{2}+\ldots t+\ldots$ . If $p(t)$ is not quadratic, enter "DNE" for each of the blanks.

Question 6

Suppose $g(x)=4 x^{2}-7 x$ . What is $g(x+h)$ ?

A) $4 x^{2}+(8 h+7) x+\left(4 h^{2}+7 h\right)$
B) $4 x^{2}+(8 h-7) x+\left(4 h^{2}-7 h\right)$
C) $4 x^{2}-(4 h-7) x-\left(4 h^{2}-7 h\right)$
D) $4 x^{2}+7 x+h$

Question 7

Suppose $g(x)=4 x^{2}-6 x$ . What is $\frac{g(x+h)-g(x)}{h}$ ?

A) $4 x+4 h-6$
B) $-4 x+4 h-6$
C) $8 x+4 h-6$
D) $-8 x+4 h-6$

Question 8

For $f(x)=x^{2}$ , does $f\left(\frac{4}{7}\right)=\frac{f(4)}{f(7)}$ ?

Question 9

Let $f(x)$ be a quadratic function which has $y$ -intercept -54 and has zeros at $x=-3$ and $x=6$ . Then $f(x)=$ ---------- $x^{2}+$ --------- $x+$ --------------

Question 10

Find a formula for the quadratic function which corresponds to the values in the following table and use it to find $g(5)$ .

Question 11

Which of the following functions are quadratic?

A) $f(m)=\sqrt{3} m^{2}+\frac{2 m}{m^{2}}-2$
B) $K(t)=(5 t-2)^{2}-6 t--27$
C) $h(t)=\frac{-7 t^{3}}{t}-3 t+10$
D) $f(x)=(x-5)^{2}-x^{2}$
E) $M(x)=3(4 x-5)(x+6)$

Question 12

Find the zeros of $F(x)=2.4 x^{2}+4.2 x+1.2$ by using the quadratic formula. List the answers in the form "A, B", with $\mathrm{A}<\mathrm{B}$ . Write your answers correct to 3 decimal places.

Question 13

The height of an object above the ground is described by the function $f(t)=2.3 t^{2}-14 t+4$ .
a) What is the initial height of the object at time $t=0$ ?
b) When does the object have height 2 ?

Question 14

Find a quadratic equation, $f$ , with zeros at $x=4$ and $x=-2$ such that $f(1)=18$ .

Question 15

Which of the following quadratic functions have zeros at $x=6$ and $x=-6$

A) $f(x)=(x-6)(x+6)$
B) $f(x)=5(x-6)(x-6)$
C) $f(x)=-9(x-6)(x+6)$
D) $f(x)=-(x+6)(x-6)$
E) $f(x)=8(x+6)(x+6)$

Question 16

Find a formula for the parabola

Question 17

The height of a baseball in feet $t$ seconds after it has been hit is given by $y=2+40 t-16 t^{2}$ .
a) What is the height of the ball 0.2 seconds after it was hit?
b) When does the ball hit the ground? (If necessary, round your answer to three decimal places)

Question 18

Is the function $h(t)=2(x-1)^{2}-6 x$ quadratic? If so, write the function in the form $h(t)=a x^{2}+b x+c$ .

Question 19

Find a formula for the quadratic function which has only one zero at $x=3$ and contains the point $(-1,-48)$

Question 20

Find a formula in terms of $f(x)=x^{2}$ for $g(x)=x^{2}+6 x+2$ .

A) $g(x)=f(x+6)-2$
B) $g(x)=f(x+3)+2$
C) $g(x)=f(x+6)-7$
D) $g(x)=f(x+3)-7$

Question 21

Select the quadratic functions that are concave upward.

A) $y=-4 x-6 x^{2}-9$
B) $y=7 x^{2}-2 x+7$
C) $4 y-5 x^{2}=-5-5 x$
D) $5 x^{2}+3 y=12$

Question 22

Is the graph of $y=4(6-4 x)(x-4)$ concave up or concave down?

Question 23

Is the graph of $y=-6(1-3 x)(x-4)$ concave up or concave down?

Question 24

Find the zeros of $y=x-5 \sqrt{x}+6$

Question 25

Is the function $f(x)=2 x^{10}-5 x^{5}+3$ quadratic?

Question 26

Suppose a quadratic function has vertex $(3,0)$ and has y-intercept 4 . Its formula can be written $y=a(x-b)^{2}$ , where $a=$ ------- and $b=$ ----------

Question 27

The graph of $r(t)=4 t^{2}-40 t+104$ has vertex (---------,--------- ) and axis of symmetry $x=$ --------

Question 28

Convert the quadratic function $y=x^{2}+10 x+28$ to vertex form. Identify the vertex and the axis of symmetry.

Question 29

Find a formula for the quadratic function whose graph has axis of symmetry $x=3.5$ , $y$ - intercept at $y=6$ , and contains the point $(1,-12)$ .

Question 30

Find a formula for the parabola:

Question 31

The height of a baseball in feet $t$ seconds after it has been hit is given by $y=2+35 t-16 t^{2}$ . At what time $t$ does the baseball reach maximum height? Give your answer correct to 3 decimal places.

Question 32

The height of a baseball in feet $t$ seconds after it has been hit is given by $y=2+35 t-16 t^{2}$ . What is the maximum height of the baseball? Give your answer correct to 3 decimal places.

Question 33

Which of the following parabolas have a vertex of $(5,-6)$ ?

A) $y=-2(x-5)^{2}-6$
B) $y=5(x+5)^{2}+6$
C) $y=-7(x+6)^{2}-5$
D) $y=4 x^{2}-40 x+94$
E) $y=6 x^{2}+60 x+156$

Question 34

Suppose a farmer has 160 feet of fence and he wants to enclose a pasture with a rectangular boundary. There is already fencing along one side of the field that he wants to enclose, so he will only need to fence 3 sides of the new field. What is the maximum area that he can fence?

Question 35

Suppose a farmer has 160 feet of fence and he wants to enclose a pasture with a rectangular boundary. There is already fencing along one side of the field that he wants to enclose, so he will only need to fence 3 sides of the new field. What are the dimension of the field that will give maximum area.

Question 36

What is the equation of the parabola that is concave down, has vertex $(-3,36)$ and contains the origin.

Question 37

Let $y=3 x^{2}-18 x+25$ .
a) Graph the function.
b) Give the vertex.
c) Give the axis of symmetry.
d) Give the y-intercept.

Question 38

How many distinct real roots does the function $y=x^{2}-4 x+7$ have?

Question 39

The vertex form of $f(x)=x^{2}+4 x-1$ is $f(x)=(x+a)^{2}-b$ , where $a=$ ----------- and $b=$ ------------

Question 40

The following figure gives the graph of $y=f(x)$ , a quadratic function with vertex (3, 2). The formula for $f(x)$ is $y=a(x-b)^{2}+c$ , where $a=$ ---------- $b=$ ----------- , and $c=$ ------------

Question 41

A relief package is dropped from an airplane and falls to the ground along a parabolic path, starting at the vertex of the parabola. The package was released when the plane was directly above a marker at a height of 5 kilometers, and the package hits the ground 4.63 kilometers from the marker. If $h$ is the height of the package when it is a horizontal distance $d$ from the marker, the equation for $h$ in terms of $d$ is given by $h(d)=a d^{2}+b d+c$ , where $a=\ldots, b=\ldots$ , and $c=\ldots$ . Round any decimals to 3 places.

Question 42

A projectile's height $h(t)$ above ground is a quadratic function of time $t$ in seconds since launched. Three values of the function are given in the table below.

What is the practical interpretation of $h(0)$ ?

A) It is the time it takes the projectile to hit the ground.
B) It is the initial speed of the projectile.
C) It is the height of the projectile above the ground the instant it is fired.
D) It is ground level.

Question 43

A projectile's height $h(t)$ above ground is a quadratic function of time $t$ in seconds since launched. Three values of the function are given in the table below.

How many seconds does it take for the projectile to hit the ground?

Question 44

A projectile's height $h(t)$ above ground in feet is a quadratic function of time $t$ in seconds since launched. Three values of the function are given in the table below.

What is the maximum number of feet above the ground that the projectile reaches?

Question 45

The formula for the following parabola is $f(x)=a(x-h)^{2}+k$ , where $a=$ -------- $h=$ --------- , and $k=$ --------

Note: Figure is not necessarily drawn to scale.

Question 46

You want to fence in a rectangular area for a dog run along the back of your home. Your home will serve as one side of the run, so you only need to purchase fencing material for the remaining three sides. The fencing material costs $\$ 1.75$ per foot, and you have a budget of $\$ 49.00$ . How many square feet are in the largest dog run you can afford to build?