Question

Rewrite the equation in vertex form by completing the square: y=4x^2+24x-7

Answer 1

Given:

`y=4x^2+24x-7`

Required:

We need to rewrite the given equation in vertex form.

Step-by-step explanation:

Consider the equation.

`y=4x^2+24x-7`
`y=2^2x^2+(2*6*2* x)-7`
`y=(2x)^2+(2*6*2x)-7`

Add and subtract 36 on the left side of the equation.

`y=(2x)^2+(2*12* x)-7+36-36`
`y=(2x)^2+(2*12* x)+36-36-7`
`y=(2x)^2+(2*12* x)+6^2-43`
`\text{ Use }a^2+2ab+b^2=(a+b)^2.\text{ Here a =2x and b=6.}`
`y=(2x+6)^2-43`

Final answer:

`y=(2x+6)^2-43`