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
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