# How do you find the x intercepts of a quadratic function?

Dec 15, 2014

A quadratic function is one of general form:
$y = a {x}^{2} + b x + c$

where a, b and c are real numbers.

This function can be plotted giving a PARABOLA (a curve in the shape of an upward or downward U)

To find the x intercepts you must put y=0; in this way you fix at zero the coordinate y of the points you are seeking.
You are left with finding the coordinate x of the points.
If y=0 you are left with: $0 = a {x}^{2} + b x + c$ which is a second degree equation.
By solving this equation you'll find two values of x (x1 and x2) that together with y=0 will give you the intercepts:
intercept 1: (x1 , 0)
intercept 2: (x2 , 0)

Remember that a second degree equation can also have solutions:
- coincident (the intercept is the VERTEX of the parabola)
- imaginary (The parabola does not cross the x axis)
Depending upon the discriminant of the equation.