In general, if you want to fi nd where a quadratic function intersects a straight line, solve the equation of the quadratic function y = f (x) = ax 2 + bx + c with the equation of the straight line l.
P 1. Finding where the quadratic function
crosses the y-axis The equation of a quadratic function is y = ax 2 + bx + c. The equation of the y-axis is x = 0. Solving the quadratic function y = ax 2 + bx + c and x = 0 gives: y = 0 + 0 + c y = c
The graph of the quadratic function crosses the y-axis at (0, c). EXAMPLE 4
Find where the following quadratic functions cross the y-axis:
(a) y = 2 x 2 + 5x − 7 (b) y = 2x + 8 − x 2
Solution (a) y = 2x 2 + 5x − 7
x = 0: y = 2(0) 2 + 5(0) − 7 = −7 It crosses the y-axis at (0, −7).
(b) y = 2x + 8 − x 2
x = 0: y = 2(0) + 8 − (0) 2 = 8 It crosses the x-axis at (0, 8).
2. Finding where the quadratic function
crosses the x-axis The equation of the x-axis is y = 0. The equation of the quadratic function is y = ax 2 + bx + c. Solving simultaneously: ax 2 + bx + c = 0
The point(s) where the graph of the quadratic function crosses the x-axis are the solutions of the quadratic equation ax 2 + bx + c = 0.
