Provide an appropriate response.
-Find a quadratic function f having x-intercepts -9 and -2 and y-intercept 6
A) $f ( x ) = x ^ { 2 } + 5 x + 6$
B) $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 11 } { 3 } x + 6$
C) $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } - \frac { 11 } { 3 } x + 6$
D) $f ( x ) = x ^ { 2 } + 11 x + 18$

Question

Provide an appropriate response.
-Find a quadratic function f having x-intercepts -9 and -2 and y-intercept 6 
A) $f ( x ) = x ^ { 2 } + 5 x + 6$
B) $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 11 } { 3 } x + 6$
C) $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } - \frac { 11 } { 3 } x + 6$
D) $f ( x ) = x ^ { 2 } + 11 x + 18$

Quizplus · Accepted Answer

A quadratic function with x-intercepts -9 and -2 can be expressed as $f(x) = a(x + 9)(x + 2)$. To find the value of $a$, we use the y-intercept (0,6), which gives us $6 = a(0 + 9)(0 + 2)$, leading to $a = \frac{1}{3}$. Thus, the correct function is $f(x) = \frac{1}{3}(x + 9)(x + 2) = \frac{1}{3}x^2 + \frac{11}{3}x + 6$.

Provide an Appropriate Response f(x)=x2+5x+6f ( x ) = x ^ { 2 } + 5 x + 6f(x)=x2+5x+6

Provide an Appropriate Response $f ( x ) = x ^ { 2 } + 5 x + 6$