Question

Write the the function f(x) = -5(x + 5)² - 2 in the form f(x) = ax² +bx+c

Answer 1

`-5(x+5)^2-2`

start expanding the squared expression using the square of a binomial,

`(a+b)^2=a^2+2\ast a\ast b+b^2`

then,

`\begin{gathered} (x+5)^2=x^2+2\ast5\ast x+5^2 \\ (x+5)^2=x^2+10x+25 \end{gathered}`

replace in the original function

`-5(x^2+10x+25)-2`

apply distributive and simplify

`\begin{gathered} -5x^2-50x-125-2 \\ -5x^2-50x-127 \end{gathered}`

Answer:

`-5x^2-50x-127`