The Intercepts of a Parabola
A yintercept of a function is a point where the graph crosses the yaxis.
That is, a yintercept is a point where x = 0.
A parabola of the form f(x) = Ax^{2} + Bx + C always has one yintercept.
To find it, let x = 0 in the equation and simplify:
Quadratic Equation.
Substitute 0 for x.
Multiply.
Add. 
f(x)
f(0) 
= Ax^{2} + Bx + C
= A(0)^{2} + B(0) + C
= 0 + 0 + C
= C 
Thus, the yintercept of f(x) = Ax^{2} + Bx + C is the point (0, C).
An xintercept of a function is a point where the graph crosses the xaxis.
That is, a point where y = 0.
A parabola of the form f(x) = Ax^{2} + Bx + C may have 0, 1, or 2
xintercepts.
Example 1
Find the y and xintercepts of the function: f(x) = x^{2}  3x  10
Solution
The yintercept is the point (0, C). Thus,
it is the point where x = 0.
Substitute 0 for x.
Simplify. 
f(x)
f(0)

= x^{2}  3x  10 = (0)^{2}
 3(0)  10
= 10 
So, the yintercept is (0, 10).
To find the xintercepts, replace f(x) with 0 and then solve for x.
Original function.
Substitute 0 for f(x). 
f(x)
0 
= x^{2}  3x  10 = x^{2}  3x  10 
To solve for x:
Factor.
Set each factor equal to 0.
Solve each equation. 
0
x + 2
x 
= (x + 2)(x  5) = 0 or x  5 = 0
= 2 or x = 5 
So, the xintercepts of f(x) = x^{2}  3x  10 are (2, 0) and (5, 0).
