# 10.3: Quadratic Equations by Square Roots

Difficulty Level:

**At Grade**Created by: CK-12Turn In

## Learning Objectives

At the end of this lesson, students will be able to:

- Solve quadratic equations involving perfect squares.
- Approximate solutions of quadratic equations.
- Solve real-world problems using quadratic functions and square roots.

## Vocabulary

Terms introduced in this lesson:

- quadratic equations involving perfect squares
- positive, negative square root
- approximate solutions
- free fall

## Teaching Strategies and Tips

Remind students that:

- \begin{align*}\sqrt{x^2}=|x|\end{align*} and is called the principal square root.
- \begin{align*}|x|=k\end{align*} implies \begin{align*}x = \pm k\end{align*}.
- Conclude that \begin{align*}x^2=c\end{align*} has two solutions when \begin{align*}c > 0\end{align*}. See Examples 1-3.
- Point out that square roots of negative numbers are not real numbers. Therefore, \begin{align*}x^2=c\end{align*} has no solutions when \begin{align*}c < 0\end{align*}.

Specify in advance the number of decimal places required of students in Examples 6 and 7 and *Review Questions* 18-22.

## Error Troubleshooting

In Example 2, show students that \begin{align*}\sqrt{\frac{16}{9}}=\frac{4}{3}\end{align*} and \begin{align*}\sqrt{\frac{1}{81}}=\frac{1}{9}\end{align*}. More square-roots of fractions can be found in *Review Questions* 4-6 and 8.

General Tip: Remind students after square-rooting both sides of an equation to include the \begin{align*}\pm\end{align*}.

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Activities
Answer Key
Answers
(45 more)
Assessment
CK.MAT.ENG.TE.1.Algebra-I.10
Common Misconceptions
completing the square
Concept Check and Troubleshooting
Differentiated Instruction
discriminant
double root
Enrichment
Inquiry Process
intercept form
line of symmetry
linear functions
linear regression
no real solutions
Pacing
parabolas
perfect squares
Problem Sets
Problem Solving
Pythagorean theorem
quadratic equation
quadratic equations
quadratic function
quadratic functions
quadratic regression
Quizzes
roots
scatter plot
Science Inquiry
Solution Key
Solutions
square roots
standard form
symmetric
Teacher Edition
Teaching Strategies
Teaching Strategies and Tips
Testing
Tests
vertex form
Worksheets
x-intercept
y-intercept
zeroes

Subjects:

Date Created:

Feb 22, 2012
Last Modified:

Aug 22, 2014
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