Question

use ( x^2 - 8x + 16 ) 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 $x^2-8x+16$, $a=1$, $b=-8$

Step2: Calculate vertex x-coordinate

Use $x=-\frac{b}{2a}$:
$x=-\frac{-8}{2(1)} = 4$

Step3: Find vertex y-coordinate

Substitute $x=4$ into $x^2-8x+16$:
$y=(4)^2-8(4)+16 = 16-32+16 = 0$

Step4: Write vertex form

Use $f(x)=a(x-h)^2+k$, where $(h,k)=(4,0)$, $a=1$:
$f(x)=1(x-4)^2+0$

Answer:

$f(x)=(x-4)^2$