9-6 solving quadratic equations 9-6by...
TRANSCRIPT
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring9-6Solving Quadratic Equations by Factoring
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Bell Quiz 9-6Find each product.
1. (x + 2)(x + 7) 2. (x – 11)(x + 5)
Factor each polynomial.
3. x2 + 12x + 35 4. x2 + 2x – 63
5. x2 – 10x + 16 10 pts possible
2 pts 2 pts
2 pts2 pts
2 pts
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Questions on 9-1
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Solve quadratic equations by factoring.
Objective
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
A method used to solve quadratic equations is to factor and use the Zero Product Property.
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Example 1A: Use the Zero Product Property
Use the Zero Product Property to solve the equation. Check your answer.
(x – 7)(x + 2) = 0
Use the Zero Product
Property.
Solve each equation.
Substitute each
solution for x into the
original equation.
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Example 1B: Use the Zero Product Property
Use the Zero Product Property to solve each equation. Check your answer.
(x – 2)(x) = 0
Use the Zero Product
Property.
Solve the second
equation.
Substitute each
solution for x into the
original equation.
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Use the Zero Product Property to solve each equation. Check your answer.
Check It Out! Example 1
1a: (x)(x + 4) = 0 1b: (x + 4)(x – 3) = 0
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
If a quadratic equation is written in standard form, ax2 + bx + c = 0, then to solve the equation, you may need to factor before using the Zero Product Property.
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
To review factoring techniques, see lessons 8-3 through 8-5.
Helpful Hint
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Example 2A: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
x2 – 6x + 8 = 0
Factor the trinomial.
Use the Zero Product
Property. Solve each equation.
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Example 2B: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
x2 + 4x = 21 The equation must be
written in standard
form. So subtract
21 from both sides.
Factor the trinomial.
Use the Zero
Product Property.
Solve each equation.
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Example 2C: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
x2 – 12x + 36 = 0
Factor the trinomial.
Use the Zero
Product Property.
Solve each equation.
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Example 2D: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
–2x2 = 20x + 50The equation must be
written in standard
form. So add 2x2 to
both sides.
Factor out the GCF 2.
Factor the trinomial.
Use the Zero Product
Property.
Solve the equation.
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
(x – 3)(x – 3) is a perfect square. Since both factors are the same, you solve only one of them.
Helpful Hint
Holt Algebra 1
9-6Solving Quadratic Equations
by FactoringCheck It Out! Example 2
Solve the quadratic equation by factoring. Check your answer.
2a: x2 – 6x + 9 = 0 2b: x2 + 4x = 5
Holt Algebra 1
9-6Solving Quadratic Equations
by FactoringCheck It Out! Example 2
Solve the quadratic equation by factoring. Check your answer.
2c: 30x = –9x2 – 25 2d: 3x2 – 4x + 1 = 0
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
�Section 9-6 (page 633) 1-6, 9, 11, 15, 18, 20, 21, 23, 25, 26, 28, 29, 41, 44, 49, 61, 62, 65