Question

X^2 + 18x = -40 + ywrite in vertex form

Answer 1

The equation in vertex form is;

`y=(x+9)^2-41`

Step-by-step explanation:

Given the equation;

`x^2+18x=-40+y`

We want to rewrite the equation in vertex form;

`f(x)=a(x-h)^2+k`

converting the equation to vertex form we have;

`\begin{gathered} x^2+18x=-40+y \\ -40+y=x^2+18x \\ y=x^2+18x+40 \\ \text{ using completing the square method;} \\ y=x^2+18x+9^2-9^2+40 \\ y=(x+9)^2-81+40 \\ y=(x+9)^2-41 \end{gathered}`

Therefore, the equation in vertex form is;

`y=(x+9)^2-41`