First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts.
-$f ( x ) = x ^ { 2 } + 18 x + 66 \quad$ Give your answers in exact form.
A) x-intercepts: $- 9 - \sqrt { 15 }$ and $- 9 + \sqrt { 15 } ; y$-intercept: 66
B) x-intercepts: $- 18 - \sqrt { 66 }$ and $- 18 + \sqrt { 66 } ;$ y-intercept: $- 66$
C) x-intercepts: $9 - \sqrt { 66 }$ and $9 + \sqrt { 66 } ; y$-intercept: 66
D) $x$-intercepts: $9 + \sqrt { 15 } ; y$-intercept: $- 66$

Question

Quizplus · Accepted Answer

To complete the square, the quadratic function $f(x) = x^2 + 18x + 66$ is rewritten as $f(x) = (x + 9)^2 - 81 + 66$, which simplifies to $f(x) = (x + 9)^2 - 15$. The x-intercepts are found by setting $f(x) = 0$ and solving for $x$, leading to $x = -9 \pm \sqrt{15}$. The y-intercept is found by evaluating $f(0)$, which is $66$.

First Rewrite the Quadratic Function in Standard Form by Completing f(x)=x2+18x+66f ( x ) = x ^ { 2 } + 18 x + 66 \quadf(x)=x2+18x+66

First Rewrite the Quadratic Function in Standard Form by Completing $f ( x ) = x ^ { 2 } + 18 x + 66 \quad$