Question

What is the connection between the solutions of the equation ax^2 + bx + c = 0 and the x intercepts of the graph f(x) = ax^2 + bx + c?

I'm confused here - aren't they the same thing except one is the equation of a quadratic equation and one is a graph?

So what is the connection between the solutions?

Answer 1

The solutions to ax^2 + bx + c = 0 , that is, the values of x which make the statement true, are the same as the x-intercepts of f(x) = ax^2 + bx + c = 0

e.g
x^2 - x - 6 = 0 has solutions x = 3 and x = -2
the graph of f(x) = x^2 - x - 6 has x-intercepts 3 and -2

https://www.wolframalpha.com/input/?i=f(x)+%3D+x%5E2+-+x+-+6