Question

Convert the function in standard form into vertex form. You must show your work. y = -x to the power of 2 + 2x + 3

Answer 1

The given function is

$y=-x^2+2x+3$

We have to complete the square to find the vertex form. First, we move the independent term

$\begin{gathered} -x^2+2x=-3 \\ x^2-2x=3 \end{gathered}$

Then, we take the linear coefficient to divide it by 2 and elevate it to the square power

$(\frac{2}{2})^2=1^2=1$

Then, we add this number on both sides

$\begin{gathered} x^2-2x+1=3+1 \\ \end{gathered}$

Now, we factor the trinomial.

$(x-1)^2=4$

Then, we move the power to the other side and we express it as a function.

Hence,

$y=-(x-1)^2+4$