Question

The graph of a quadratic function (a parabola) has x-intercepts -1 and 3 and a range of all numbers less than or equal to 4. Write an equation for the function.

Answer 1

Well, the x-intercepts correspond to real roots, right? And real roots correspond to factors, e.g., if c is a root of the quadratic, then x-c is a factor.

So you know 2 roots, hence you know 2 factors. That will give you A quadratic equation, and if it doesn't produce the right vertex, then you just need to multiply it by a constant. :)

Answer 2

I should add - you know the vertex, since you know the range (the max or min or the range is the y-coordinate of the vertex) and you know the two x-intercepts (the axis of symmetry is halfway between the 2)

Answer 3

Thanks!

Answer 4

You're welcome. Happy to help! :)