Question

Please help:Consider the function f (x) = x^2 + 4x + 7.Which equation shows function f written in vertex form?A. f (x) = (x+2)^2 + 3B. f (x) = (x+4)^2 + 11C. f (x) = (x+3)^2 + 7D. f (x) = (x+4)^2 − 7

Answer 1

we have the function

$f(x)=x^2+4x+7$

Convert the given equation into vertex form

Complete the square

so

$\begin{gathered} f(x)=(x^2+4x)+7 \\ f(x)=(x^2+4x+2^2-2^2)+7 \\ f(x)=(x+2)^2+3 \end{gathered}$

The answer is option A (vertex at (-2,3)