Question

use (-x^2 + 2x + 5) to answer the following questions.
(x = -\frac{b}{2a})
use your value of (x) in the equation to find the (y)-coordinate of the vertex.
(f(x) = a(x - h)^2 + k)

1. rewrite the quadratic in vertex form.

type a response

Explanation:

Step1: Identify a, b values

For $-x^2 + 2x + 5$, $a=-1$, $b=2$

Step2: Find vertex x-coordinate

Use $x=-\frac{b}{2a}$
$x=-\frac{2}{2(-1)} = 1$

Step3: Find vertex y-coordinate

Substitute $x=1$ into original equation:
$y=-(1)^2 + 2(1) + 5 = -1 + 2 + 5 = 6$

Step4: Write vertex form

Vertex form is $f(x)=a(x-h)^2+k$, where $(h,k)=(1,6)$, $a=-1$
$f(x)=-1(x-1)^2 + 6$

Answer:

$f(x)=-(x-1)^2 + 6$