Question

section 05.1: problem 4 (4 points) rewrite the quadratic function f(x)=4x² + 8x + 1 in standard form, f(x)=a(x - h)² + k, and give the vertex. f(x)= (x - )²+ help (numbers) · vertex: help (points) note: you can earn partial credit on this problem. note: you are in the reduced scoring period. all work counts for 70% of the original. preview my answers submit answers show me another you have attempted this problem 0 times. you have unlimited attempts remaining. email instructor

Explanation:

Step1: Factor out the coefficient of $x^{2}$

$f(x)=4(x^{2} + 2x) + 1$

Step2: Complete the square inside the parentheses

For the expression $x^{2}+2x$, we know that $(x + m)^{2}=x^{2}+2mx+m^{2}$. Here $2m = 2$, so $m = 1$ and $x^{2}+2x=(x + 1)^{2}-1$. Then $f(x)=4((x + 1)^{2}-1)+1$.

Step3: Expand and simplify

$f(x)=4(x + 1)^{2}-4 + 1=4(x+1)^{2}-3$.

Answer:

$f(x)=4(x + 1)^{2}-3$, Vertex: $(-1,-3)$