Given:
[tex]y=4x^2+24x-7[/tex]Required:
We need to rewrite the given equation in vertex form.
Explanation:
Consider the equation.
[tex]y=4x^2+24x-7[/tex][tex]y=2^2x^2+(2\times6\times2\times x)-7[/tex][tex]y=(2x)^2+(2\times6\times2x)-7[/tex]Add and subtract 36 on the left side of the equation.
[tex]y=(2x)^2+(2\times12\times x)-7+36-36[/tex][tex]y=(2x)^2+(2\times12\times x)+36-36-7[/tex][tex]y=(2x)^2+(2\times12\times x)+6^2-43[/tex][tex]\text{ Use }a^2+2ab+b^2=(a+b)^2.\text{ Here a =2x and b=6.}[/tex][tex]y=(2x+6)^2-43[/tex]Final answer:
[tex]y=(2x+6)^2-43[/tex]