Question

Use the vertex formula to find the vertex of the quadratic function f(x) = – x² + 6x - 10.The vertex is(Type an ordered pair. Simplify your answer.)

Answer 1

We have the equation of the quadratic function:

$-x^2+6x-10$

We have to use the vertex formula to calculate the vertex. If h is the x-coordinate of the vertex, we can calculate it as:

$h=\frac{-b}{2a}=\frac{-6}{2\cdot(-1)}=\frac{-6}{-2}=3$

Then, we can calculate the y-coordinate replacing h in the equation:

$\begin{gathered} y_v=-h^2+6h-10=-3^2+6(3)-10 \\ y_v=-9+18-10=-1 \end{gathered}$

The vertex has coordinates (x,y) = (3,-1).