Question

What are the x-intercepts of the graph of the function f(x) = x2 + 4x -12?

Answer 1

First thing to notice is that we're dealing with a parabola, so we know it has a vertex, vertical axis of symmetry, etc.

Always factor if possible.

Start by finding the roots. If 0 = (x-1)(x+5), then x = 1 or -5.

Now hit up the y-intercept.  If x = 0,  .

The vertex is going to be right between the roots, so average them: .  The axis of symmetry is x -2.

So the vertex is at x = -2, and y =  .  (-2, -9).

To find another point on the graph, you just choose a random x.  How about 3.  .... (3, 16)