Question

Write the equation of a quadratic function with roots at 1 and 5 and a vertex at (3,-2)

Answer 1

The equation of a parabola is the following:

$(y - k) = a(x - h)^{2}$

where $(h, k)$ is the coordinate of the vertex and $a$ is a constant. With the information you have above, you are able to fill in $(h, k)$ and solve for $a$ with the information that $(1, 0)$ and $(5, 0)$ are roots of the equation.