Question

section 05.1: problem 4 (4 points) results for this submission 1 of the answers is not correct. 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)=4(x - 1)²+ - 3 help (numbers) · vertex (-1,-3) help (points) hint 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 your score was recorded. scores are sent to d2l brightspace every 24 hours. you have attempted this problem 2 times you received a score of 52% for this attempt your overall recorded score is 52%. you have unlimited attempts remaining.

Explanation:

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

$$
LATEXBLOCK0
$$

Step2: Complete the square inside the parentheses

For the quadratic 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

$$
LATEXBLOCK1
$$

The standard - form of a quadratic function is $f(x)=a(x - h)^{2}+k$, where the vertex is $(h,k)$. For the function $f(x)=4(x + 1)^{2}-3$, we have $h=-1$ and $k=-3$.

Answer:

The standard form is $f(x)=4(x + 1)^{2}-3$ and the vertex is $(-1,-3)$