Question

what value of m does the graph y = 18x2 + mx + 2 have exactly one x-intercept?

Answer 1

A parabola has only one x-intercept if its vertex touches the x-axis but does not cross it, meaning if the parabola has an x-intercept at \(x=x_0\), the parabola doesn't go lower (or higher, depending on the "direction") that the point \((x_0,0)\).

So, a parabola in the general form \(ax^2+bx+c\) can be written in vertex form as \(a(x-h)^2+k\) with \(k=0\).

This means you have to find a value of \(m\) such that the given parabola can be factored as a perfect square trinomial.