89.1k views
2 votes
Rewrite the function f(x) = -2(x+2)²-11 in the form f(x) = ax²+bx+c.
X
S

Rewrite the function f(x) = -2(x+2)²-11 in the form f(x) = ax²+bx+c. X S-example-1
User Utek
by
7.4k points

2 Answers

4 votes

Answer:


\huge\boxed{\sf f(x) = -2x\² - 8x - 19}

Explanation:

Given function:

f(x) = -2(x + 2)² - 11

Using formula: (a + b)² = a² + 2ab + b²

f(x) = -2[(x)² + 2(x)(2) + (2)²] - 11

f(x) = -2(x² + 4x + 4) - 11

Distribute

f(x) = -2x² - 8x - 8 - 11

f(x) = -2x² - 8x - 19


\rule[225]{225}{2}

User Ashtav
by
8.4k points
4 votes

Answer:


\displaystyle{f(x)=-2x^2-8x-19}

Explanation:

Given the vertex equation:


\displaystyle{f(x)=-2(x+2)^2-11}

First, apply the perfect square formula, expanding to standard form:


\displaystyle{f(x)=-2(x^2+4x+4)-11}

Expand -2 in:


\displaystyle{f(x)=-2x^2-8x-8-11}

Evaluate or simplify:


\displaystyle{f(x)=-2x^2-8x-19}

Hence,


\displaystyle{f(x)=-2x^2-8x-19}

User Kromster
by
8.4k points