Question

How do you find the vertex and the intercepts for `y=x^2+10x`?

Answer 1

The x-intercepts can be found by factoring: y = x(x+10) and using the Zero Product Property.

Explanation:

Thus, x = 0 and x = -10 are the x-intercepts.
Because of the symmetry of the parabola, the vertex is found halfway between those two points, at x = -5. (The line of symmetry is actually x = -5!)

So, substitute in x = -5 and evaluate: y = -5(-5+10) = -25.
The vertex is at (5,-25).

In case you were also interested in the y-intercept, substitute in x = 0 and evaluate: y = 0(0+10) = 0. (0,0) is both a y- and x-intercept!