MCF 3M1
Date ___________
Lesson 2: Solving Quadratic Equations by Graphing
A quadratic equation is any equation that contains a polynomial whose highest degree is 2.
For example, x 2  8 x  15  0 .
Quadratic equations can be solved by graphing the corresponding function f ( x)  ax 2  bx  c .
The solutions or roots of the functions are the zeros, or x-intercepts.
Example 1
Determine the solutions of the quadratic equation x 2  8 x  12  3 by graphing.
Rearrange the Equation to Determine the Zeros in the Corresponding Graph
Graph:
Equation:
Solutions:
Example 2
Determine the solutions of the quadratic equation x 2  8 x  12  3 by graphing.
Determining the Points of Intersection of Two Corresponding Functions
Graph:
Equation:
Solutions:
MCF 3M1
Date ___________
Example 3
A ball is tossed upward from a cliff that is 40 m above water. The height of the ball above the
water is modeled by h(t )  5t 2  10t  40 , where h(t ) is the height in metres and t is the time in
seconds. Use a graph to answer the following questions:
a) What is the maximum height reached by the ball?
b) When will the ball hit the water?