Presentation on theme: "I can use the zero product property to solve quadratics by factoring"— Presentation transcript:
1I can use the zero product property to solve quadratics by factoring Solving by factoring
2Warm Up 1. f(x) = x2 - 6x + 8 2. f(x) = -x2 – 2x + 3 Use your calculator to find the x-intercept of each function.1. f(x) = x2 - 6x + 82. f(x) = -x2 – 2x + 3Factor each expression.3. 3x2 – 12x3x(x – 4)4. x2 – 9x + 18(x –6)(x –3)5. x2 – 49(x –7)(x +7)
3ConnectionsWe find zeros on a graph by looking at the x-intercepts or viewing the table and identifying the x-intercept as the point where y=0.Using this knowledge determine how one could find the zeros of a quadratic algebraically. Share your method with your partner.Use f(x) = x2 – 3x – 18 to help your discussion.
4You can find the roots of some quadratic equations by factoring and applying the Zero Product Property.Functions have zeros or x-intercepts.Equations have solutions or roots.Reading Math
5Example 2A: Finding Zeros by Factoring Find the zeros of the function by factoring.f(x) = x2 – 4x – 12x2 – 4x – 12 = 0Set the function equal to 0.(x + 2)(x – 6) = 0Factor: Find factors of –12 that add to –4.x + 2 = 0 or x – 6 = 0Apply the Zero Product Property.x= –2 or x = 6Solve each equation.
6Example 2B: Finding Zeros by Factoring Find the zeros of the function by factoring.g(x) = 3x2 + 18x3x2 + 18x = 0Set the function to equal to 0.3x(x+6) = 0Factor: The GCF is 3x.3x = 0 or x + 6 = 0Apply the Zero Product Property.x = 0 or x = –6Solve each equation.
7Check It Out! Example 2aFind the zeros of the function by factoring.A.f(x)= x2 – 5x – 6B.g(x) = x2 – 8x
8Quadratic expressions can have one, two or three terms, such as –16t2, –16t2 + 25t, or –16t2 + 25t + 2. Quadratic expressions with two terms are binomials. Quadratic expressions with three terms are trinomials. Some quadratic expressions with perfect squares have special factoring rules.
9Example 4B: Find Roots by Using Special Factors Find the roots of the equation by factoring.18x2 = 48x – 3218x2 – 48x + 32 = 0Rewrite in standard form.2(9x2 – 24x + 16) = 0Factor. The GCF is 2.9x2 – 24x + 16 = 0Divide both sides by 2.(3x)2 – 2(3x)(4) + (4)2 = 0Write the left side as a2 – 2ab +b2.(3x – 4)2 = 0Factor the perfect-square trinomial.3x – 4 = 0 or 3x – 4 = 0Apply the Zero Product Property.x = or x =Solve each equation.
10Example 4A: Find Roots by Using Special Factors Find the roots of the equation by factoring.4x2 = 254x2 – 25 = 0Rewrite in standard form.(2x)2 – (5)2 = 0Write the left side as a2 – b2.(2x + 5)(2x – 5) = 0Factor the difference of squares.2x + 5 = 0 or 2x – 5 = 0Apply the Zero Product Property.x = – or x =Solve each equation.
11Check It Out! Example 4aFind the roots of the equation by factoring.A. x2 – 4x = –4B. 25x2 = 9
12Example 5: Using Zeros to Write Function Rules Write a quadratic function in standard form with zeros 4/3 and –7. Your factors should not include fractions.
13Check It Out! Example 5Write a quadratic function in standard form with zeros 5/2 and –5. Your factors should not include fractions.
14Could you develop more than one quadratic with the same zeros? If yes give an example use the zeros 2 and 4.If no explain why.