In the previous unit we graphed quadratic equations, this unit will focus on several ways in which we can solve quadratic equations. The first method we will use is graphing.
What You Will Learn:
*Solve quadratic equations by graphing.
*Use graphs to fi nd and approximate the zeros of functions.
Number of Solutions of a Quadratic Equation
A quadratic equation has:
• no real solutions when the graph of its related function has no x-intercepts
• one real solution when the graph of its related function has one x-intercept.
• two real solutions when the graph of its related function has two x-intercepts.
Solving Quadratic Equations by Graphing
Step 1 Write the equation in standard form, ax2 + bx + c = 0.
Step 2 Graph the related function y = ax2 + bx + c.
Step 3 Find the x-intercepts, if any. The solutions, or roots, of ax2 + bx + c = 0 are the x-intercepts of the graph.
Question 1
1.
The solution(s) are : (answer format: x = _____ and x = _____)
Question 2
2.
The solution is: (answer format: x = _____ )
Question 3
3.
Finding Zeros of Functions
Recall that a zero of a function is an x-intercept of the graph of the function.