Question

use $2x^2 + 8x + 13$ 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 $2x^2+8x+13$, $a=2$, $b=8$

Step2: Calculate vertex x-coordinate

Use $x=-\frac{b}{2a}$:
$x=-\frac{8}{2\times2}=-\frac{8}{4}=-2$

Step3: Find vertex y-coordinate

Substitute $x=-2$ into $2x^2+8x+13$:
$y=2(-2)^2+8(-2)+13=2(4)-16+13=8-16+13=5$

Step4: Write vertex form

Use $f(x)=a(x-h)^2+k$, where $h=-2$, $k=5$, $a=2$:
$f(x)=2(x-(-2))^2+5=2(x+2)^2+5$

Answer:

$2(x+2)^2+5$