For this case we must change the following equation:
[tex]y = a (x-h) ^ 2 + k[/tex] to the standard form: [tex]y = ax ^ 2 + bx + c[/tex]
By definition we have to:
[tex](a-b) ^ 2 = a ^ 2-2ab + b ^ 2[/tex]
Then, rewriting:
[tex]y = 4 (x-5) ^ 2 + 7\\y = 4 (x ^ 2-2 * 5 * x + 5 ^ 2) +7[/tex]
Applying distributive property to the terms within parentheses:
[tex]y = 4x ^ 2-40x + 100 + 7[/tex]
Finally we have:
[tex]y = 4x ^ 2-40x + 107[/tex]
Answer:
[tex]y = 4x ^ 2-40x + 107[/tex]
