Activity
Solve each equation. Be prepared to explain or show your reasoning.
Enter the solution(s) to the equation.
Compare your answer:
and
Enter the solution(s) to the equation.
Compare your answer:
and
Enter the solution(s) to the equation.
Compare your answer:
Enter the solution(s) to the equation.
Compare your answer:
and
Enter the solution(s) to the equation.
Compare your answer:
No solution
Enter the solution(s) to the equation.
Compare your answer:
and
Video: Choosing an Effective Strategy to Solve Quadratic Equations
Watch the following video to learn more about choosing an effective strategy to solve quadratic equations.
Self Check
Additional Resources
Choosing an Effective Strategy to Solve Quadratic Equations
You have learned various strategies to solve quadratic equations in different forms. If possible, try to use reasoning before graphing an equation.
Let's look at some examples.
Using Reasoning and the Square Root Property
Equations such as these can be solved by reasoning and using the square root property.
Example 1
and
Example 2
and
Example 3
and
Each equation above is different in some way, but they all can be solved using the same process.
Using Reasoning and the Zero Product Property
Equations such as these can be solved by reasoning and using the zero product property.
Example 1
and
Example 2
and
Using Graphing to Solve
Some equations might require graphing to be solved. One method is to rearrange the equation such that it is in the form of expression . Then graph =expression, and find the -intercepts to identify the solutions.
Given:
Step 1 - Rewrite the equation to set it equal to 0.
Step 2 - Graph the equation with = the expression that equals zero.
Graph .
Step 3 - Identify the -intercepts from the graph.
This graph has two -intercepts at and .
The original equation has two solutions at and .
Try it
Try It: Choosing an Effective Strategy to Solve Quadratic Equations
Solve each equation using any method.
1.
Here is how to choose an effective strategy and use it to solve quadratic equations:
and
2.
Here is how to choose an effective strategy and use it to solve quadratic equations:
and