Question

Megan wants to find the minimum value of the function y=x^2-10x+3 . She begins to convert the equation into vertex form by completing the square. Megan stops at the step below.y=(x+a)^2 +3 + bWhat number should Megan use to replace the a in this equation?-1025-5100

Answer 1

Okay, here we have this:

Considering the provided function, we are going to convert it to vertex form by completing the square to identify what number should Megan use to replace the a in the equation, so we obtain the following:

Then we will first write the function in the form: x^2+2ax+a^2. We have:

2a=-10

a=-10/2

a=-5

Then:

`\begin{gathered} x^2-10x+3+(-5)^2-(-5)^2 \\ =(x-5)^2+3-(-5)^2 \end{gathered}`

Finally we obtain that Megan should use "-5" to replace the a in this equation.