Question

if the vertex of a quadratic functions is on the x-axis, what must be true about the number of x-intercepts? How do you know?

Answer 1

Vertex form of parabola

• y=a(x-h)²+k

Where

• vertex=(h,k)

So

if vertex is on x axis k is 0 and the parabola has only 1 x intercept

The form will be

• y=a(x-h)²

Answer 2

x-intercepts are points at which the curve intercepts the x-axis, so when y = 0.

If the vertex of a quadratic function is on the x-axis, there will be only one x-intercept since the parabola will intersect the x-axis at one point only.

If the vertex of the function touches the x-axis, the zero at this point will have a multiplicity of two. For example, if the vertex is at (4, 0), and therefore the zero is at x = 4, then the function will be
`y=a(x - 4)^2` (where a is some constant).