Question

Instructions: Given the function in standard form, use completing the square to write the function in vertex form and then identify the vertex.

Answer 1

Given the function in standard form:

$y=x^2+6x-3$

• First, we need to find the vertex, V = (h, k), as follows:

$h=\frac{-b}{2a}$

where a = 1, b = 6, and c = -3; then:

$h=\frac{-6}{2}=-3$$\begin{gathered} k=f(-3) \\ k=(-3)^2+6(-3)-3 \\ k=-12 \end{gathered}$

The vertex of the quadratic function is V = (-3, -12).

• Vertex form of the quadratic function:

$y=a\left(x-h\right)^2+k$

Replacing in the equation:

$y=(x+3)^2-12$