Algebra

9.1 Solving Quadratic Equations

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

Algebra

Objective

Algebra

9.1 Solving Quadratic Equations

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)

Algebra

9.1 Solving Quadratic EquationsExample 1: Evaluating Expressions Involving Square

RootsEvaluate the expression.

Evaluate the square root.

Add.= 25Multiply.= 18 + 7

3 36 + 7

3 36 + 7 = 3(6) + 7

Algebra

9.1 Solving Quadratic EquationsGuided Practice

Evaluate the expression.

Evaluate the square root.

Add.= 14

Multiply.= 10 + 4

2 25 + 4

2 25 + 4 = 2(5) + 4

Algebra

9.1 Solving Quadratic EquationsHow 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

Algebra

9.1 Solving Quadratic EquationsSummary

• 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

Algebra

9.1 Solving Quadratic EquationsEvaluating Radical Equations

Solve the equation.

Original ProblemTake square root of both sides

Simplify

x 2 64

x 2 64x 8

Algebra

9.1 Solving Quadratic EquationsGuided Practice

Solve the equation.

x 2 256

Algebra

9.1 Solving Quadratic EquationsEvaluating Multi-Step Radical Equations

Solve the equation.Original ProblemSubtract 4 from both sidesDivide both sides by 2

Take square root of both sidesSimplify

2x 2 4 76

2x 2 72

x 2 36

x 2 36x 6

Algebra

9.1 Solving Quadratic EquationsGuided Practice

Solve the equation.

3x 2 4 143

Algebra

9.1 Solving Quadratic EquationsApplication: 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?

Algebra

9.1 Solving Quadratic EquationsApplication: Falling Objects

h = -16t2 + s Equation0 = -16t2 + 1600 Substitute-1600 = -16t2 Subtract 1600t2 = 100 Dividet = ±10 Square Roott = 10 seconds Time is positive

Algebra

9.1 Solving Quadratic EquationsLesson Quiz

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