1. Objective
I will use square roots to evaluate radical expressions and equations.
Algebra

2. Vocabulary
• Quadratic Equation - an equation that can be written in standard form as:
ax2 + bx + c = 0, where a ≠ 0
• Leading Coefficient - the coefficient (number that precedes) the first term in standard form (x2)

3. Example 1: Evaluating Expressions Involving Square Roots
Evaluate the expression.
= 3(6) + 7
Evaluate the square root. =
Multiply.
= 25
Add.

4. Guided Practice Evaluate the expression. 2 25 + 4 2 25 + 4 = 2(5) + 4
= 2(5) + 4
Evaluate the square root. =
Multiply.
= 14
Add.

5. How to Solve a Quadratic Equation
When b = 0 and the equation is in the form of ax2 + c = 0:
isolate x2 (move c to the other side, then a)
solve for x by finding the square root of both sides of the equation

6. Summary Solving x2 = d by finding square roots:
If d > 0, then x2 has two solutions (+, -)
If d = 0, then x2 has one solution (0)
If d < 0, then x2 has no real solutions

7. Evaluating Radical Equations
Solve the equation.
Original Problem
Take square root of both sides
Simplify

8. Guided Practice
Solve the equation.

9. Evaluating Multi-Step Radical Equations
Solve the equation.
Original Problem
Subtract 4 from both sides
Divide both sides by 2
Take square root of both sides
Simplify

10. Guided Practice
Solve the equation.

11. Application: Falling Objects
The height of a falling object can be found using the equation h = -16t2 + s, where h is the height in feet, t is the time in seconds, and s is the initial height in feet. If an object is dropped from 1600 feet, when will it reach the ground?

12. Application: Falling Objects
h = -16t2 + s Equation
0 = -16t Substitute
-1600 = -16t2 Subtract 1600
t2 = Divide
t = ±10 Square Root
t = 10 seconds Time is positive

13. Lesson Quiz
Solve the equation.
1. x2 = x2 + 8 = 152