solving quadratic equations by graphing and factoring

x = 5 or x = –5 Write the zeros as solutions for two equations. The graph shows the original zeros of 4 and –7.Ģ4 Write a quadratic function in standard form with zeros 5 and –5.Ĭheck It Out! Example 5 Write a quadratic function in standard form with zeros 5 and –5. f(x) = x2 + 3x – 28 Replace 0 with f(x).Įxample 5 Continued 10 –35 –10 Check Graph the function f(x) = x2 + 3x – 28 on a calculator. (x – 4)(x + 7) = 0 Apply the converse of the Zero Product Property to write a product that equals 0. x – 4 = 0 or x + 7 = 0 Rewrite each equation so that it equals 0. x = 4 or x = –7 Write the zeros as solutions for two equations. Write a quadratic function in standard form with zeros 4 and –7. –1 10 1Ģ1 If you know the zeros of a function, you can work backward to write a rule for the functionĢ2 Example 5: Using Zeros to Write Function Rules The function appears to have zeros at and. x = or x = Solve each equation.Ĭheck Graph the related function f(x) = 25x2 – 9 on a graphing calculator. 5x + 3 = 0 or 5x – 3 = 0 Apply the Zero Product Property. (5x + 3)(5x – 3) = 0 Factor the difference of squares. 25x2 = 9 25x2 – 9 = 0 Rewrite in standard form. –3 30 3 10ġ9 Find the roots of the equation by factoring.Ĭheck It Out! Example 4b Find the roots of the equation by factoring. 4x2 = 25ġ8 Example 4 Continued Check Graph the related function f(x) = 4x2 – 25 on a graphing calculator. Some quadratic expressions with perfect squares have special factoring rules.ġ7 Example 4A: Find Roots by Using Special Factorsįind the roots of the equation by factoring. Quadratic expressions with three terms are trinomials. Quadratic expressions with two terms are binomials. Check Substitute each value into original equation. x = 0 or x = 8 Solve each equation.įind the zeros of the function by factoring. x = 0 or x – 8 = 0 Apply the Zero Product Property. g(x) = x2 – 8x x2 – 8x = 0 Set the function to equal to 0. x2 – 5x – 6 = 0 x2 – 5x – 6 = 0 (–1)2 – 5(–1) – 6 (6)2 – 5(6) – 6 36 – 30 – 6 1 + 5 – 6  ġ4 Find the zeros of the function by factoring.Ĭheck It Out! Example 2b Find the zeros of the function by factoring. x = –1 or x = 6 Solve each equation.įind the zeros of the function by factoring. x + 1 = 0 or x – 6 = 0 Apply the Zero Product Property. (x + 1)(x – 6) = 0 Factor: Find factors of –6 that add to –5. f(x)= x2 – 5x – 6 x2 – 5x – 6 = 0 Set the function equal to 0. x = 0 or x = –6 Solve each equation.ġ1 Check Check algebraically and by graphing.Įxample 2B Continued Check Check algebraically and by graphing. 3x = 0 or x + 6 = 0 Apply the Zero Product Property. g(x) = 3x2 + 18x 3x2 + 18x = 0 Set the function to equal to 0. x= –2 or x = 6 Solve each equation.ĩ Find the zeros of the function by factoring.Įxample 2A Continued Find the zeros of the function by factoring. x + 2 = 0 or x – 6 = 0 Apply the Zero Product Property. (x + 2)(x – 6) = 0 Factor: Find factors of –12 that add to –4. f(x) = x2 – 4x – 12 x2 – 4x – 12 = 0 Set the function equal to 0. Reading Mathįind the zeros of the function by factoring. Zeros are -3 and 1ħ You can find the roots of some quadratic equations by factoring and applying the Zero Product Property.

The zeros are 2 and 4Ħ Check It Out! Example 1 Find the zeros of g(x) = –x2 – 2x + 3 by using a graph and a table. These zeros are always symmetric about the axis of symmetry.ĥ Example 1: Finding Zeros by using your graphing calculatorįind the zeros of f(x) = x2 – 6x + 8 by using a graph and zero function on your calculator. Unlike linear functions, which have no more than one zero, quadratic functions can have two zeros, as shown at right. The zeros of a function are the x-intercepts. x2 – 49 (x – 7)(x + 7)ģ Objectives Solve quadratic equations by graphing or factoring.ĭetermine a quadratic function from its roots.Ĥ A zero of a function is a value of the input x that makes the output f(x) equal zero. Lesson Presentation Lesson Quiz Holt Algebra 2Ģ Warm Up Find the x-intercept of each function. Presentation on theme: '5-3 Solving Quadratic Equations by Graphing and Factoring Warm Up'- Presentation transcript:ġ 5-3 Solving Quadratic Equations by Graphing and Factoring Warm Up

Solving quadratic equations by graphing and factoring