Question

read. Kuta Software - Infinite Algebra 2 Vertex Form of Parabolas Use the information provided to write the vertex form equation of each parabola. 2) yox – 2x-5 Name Samantha sherlar 1) y = x² + 16x + 71 zalxk) 24

Answer 1

Given the function:

`y=x^2+16x+71`

We need to find the vertex of the parabola

So, we will complete the square of the function as follows:

`\begin{gathered} y=x^2+16x+71+((16)/(2))^2-((16)/(2))^2 \\ \\ y=x^2+16x+71+64-64 \\ y=(x^2+16x+64)+(71-64) \\ \\ y=(x+8)^2+7 \end{gathered}`

The general equation of the parabola has the form:

`y=(x-h)^2+k`

Where ( h, k) is the coordinates of the vertex

By comparing the equations:

`\begin{gathered} x-h=x+8 \\ -h=8 \\ h=-8 \\ k=7 \end{gathered}`

So, the answer will be:

The coordinates of the vertex = ( -8, 7)