Question

f(x)= 4x^2+10x+10
Express f(x) in the form (ax+b)^2+c.

Answer 1

(2x+5)^2-15

Answer 2

\[
f(x)=4x^2+10x+10\\
f(x)=(2x)^2+\color{red}{2(4x)\left(\frac{10}{8}\right)}+10\\
\text{this we have to make of the form:}\\
(a+b)^2=a^2+2ab+b^2\\
\text{we obtain:}\quad b=\frac{10}{8}={5\over2}\\
f(x)=(2x)^2+2(4x)\left(5\over2\right)\color{red}{+\left(5\over2\right)^2-\left(5\over2\right)^2}+10\\
\]now, put the things together

Answer 3

whoops...
\[
f(x)=4x^2+10x+10\\
f(x)=(2x)^2+\color{red}{2(2x)\left(\frac{10}{4}\right)}+10\\
\text{this we have to make of the form:}\\
(a+b)^2=a^2+2ab+b^2\\
\text{we obtain:}\quad b=\frac{10}{4}={5\over2}\\
f(x)=(2x)^2+2(4x)\left(5\over2\right)\color{red}{+\left(5\over2\right)^2-\left(5\over2\right)^2}+10\\
\]

Answer 4

you follow?

Answer 5

Yes. Thank you. I did it the way @positron did. So my answers were all wrong.