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

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Presentation transcript:

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

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)

Example 1: Evaluating Expressions Involving Square Roots Evaluate the expression. 3 36 + 7 3 36 + 7 = 3(6) + 7 Evaluate the square root. = 18 + 7 Multiply. = 25 Add.

Guided Practice Evaluate the expression. 2 25 + 4 2 25 + 4 = 2(5) + 4 2 25 + 4 2 25 + 4 = 2(5) + 4 Evaluate the square root. = 10 + 4 Multiply. = 14 Add.

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

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

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

Guided Practice Solve the equation.

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

Guided Practice Solve the equation.

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?

Application: Falling Objects h = -16t2 + s Equation 0 = -16t2 + 1600 Substitute -1600 = -16t2 Subtract 1600 t2 = 100 Divide t = ±10 Square Root t = 10 seconds Time is positive

Lesson Quiz Solve the equation. 1. x2 = 16 2. x2 + 8 = 152