Question

Rewrite the function f(x) = -2(x+2)²-11 in the form f(x) = ax²+bx+c.
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Answer 1

`\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}`

Answer 2

`\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}`