1. Lesson 1

1.9. Explore 4

Mathematics 20-1 Module 4

Module 4: Quadratic Equations and Inequalities

 

Two Methods for Solving Quadratic Equations

 

Retrieve your work from Try This 1 and Share 1. You investigated a quadratic equation representing the height of a spear over time. Revisit your answer from Share 2 question 2. You were asked to solve the quadratic equation 3 = −1.42t2 + 3.75t + 1.53. You can solve this equation in a number of ways. Two possible methods are described here.

 

Method 1: The Zero Method

 

You can solve this equation by rearranging the equation so that all of the terms are on one side.

 

 


The solution to this rearranged equation is seen when the function on the right side is equal to zero.

 

Graphically, the roots of the equation are the zeros of the quadratic function. You can find the zeros using any of the graphing methods previously encountered.

 

This is the graph of a parabola opening down with approximate x-intercepts of 0.48 and 2.16.

 

Method 2: Graphing a Related System of Equations

 

This is a play button that opens Solving a Quadratic Equation by Graphing a Related System of Equations.

There is another way to solve this problem graphically. Watch Solving a Quadratic Equation by Graphing a Related System of Equations to see Method 2.

 


 

Self-Check 3

 

This is a play button that opens Solving Quadratic Equations Self-Check.

Take a moment to check your understanding of the concepts presented so far. Complete Solving Quadratic Equations Self-Check. The questions are not for marks; instead, they are provided for you to assess your own learning. Have some scrap paper handy to do rough work. You may wish to save your rough work in your course folder for future reference. If you make a mistake, don’t worry! You can reset the question and then try again!