Question

I have a question on my homework asking for a equation with a vertex of (3,-2) that has no x-intercepts. I have no idea where to begin with this equation besides vertex form. I don't know where to go from there.

Answer 1

The given vertex is (3,-2), so we can use the standard form to find the equation

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

Assuming that a = 1, let's replace the given values of the vertex

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

However, a must be negative so the parabola has no x-intercepts.

Hence, the answer to (a) is

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

The solutions of this equation above are not real numbers because there aren't x-intercepts. In other words, the discriminant is negative.

To answer part b, we have to say that a is positive, so the equation is

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