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) $f ( x ) = x ^ { 2 } + 11 x + 18$
D) $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } - \frac { 11 } { 3 } x + 6$

Question

Quizplus · Accepted Answer

A quadratic function with given x-intercepts $a$ and $b$ can be expressed as $f(x) = k(x - a)(x - b)$, where $k$ is a constant. For x-intercepts $-9$ and $-2$, the function is $f(x) = k(x + 9)(x + 2)$. Given the y-intercept is 6, we substitute $x = 0$ to find $k$: $f(0) = k(0 + 9)(0 + 2) = 6$, which simplifies to $18k = 6$, giving $k = \frac{1}{3}$. Thus, the function is $f(x) = \frac{1}{3}(x + 9)(x + 2)$, which simplifies to $f(x) = \frac{1}{3}x^2 + \frac{11}{3}x + 6$.

Provide an Appropriate Response fff Having xxx -Intercepts −9- 9−9 And −2- 2−2 And yyy

Provide an Appropriate Response $f$ Having $x$ -Intercepts $- 9$ And $- 2$ And $y$