Question

What are the coordinates of the vertex of the parabola y= x2 + 4x – 6?

Answer 1

We have the equation of a parabola.

We can express the coordinates of the vertex (h,k) using the coefficients of the parabola:

$\begin{gathered} h=-\frac{b}{2a} \\ k=f(h) \end{gathered}$

As the parabola is y=x²+4x-6, the expression for h and k is:

$\begin{gathered} h=-\frac{b}{2a}=-\frac{4}{2\cdot1}=-2 \\ k=f(-2)=(-2)^2+4\cdot(-2)-6=4-8-6=-10 \end{gathered}$

Then, the coordinates of the vertex are (h,k) = (-2,-10).

Answer: The vertex is (-2,-10)