5.2 Solving From Factored Form PDF
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2022
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This document appears to be a set of notes or practice problems related to solving quadratic equations from factored form. It includes examples and exercises that cover various forms of quadratic equations. The solutions also include sketches and explain the concepts of roots and zeros relating to functions.
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5.2 Solving From Factored Form FULL.notebook November 28, 2022 5.2 Solving From Factored Form Recall: Equations in Factored Form Where are the zeros/ x‐intercepts?...
5.2 Solving From Factored Form FULL.notebook November 28, 2022 5.2 Solving From Factored Form Recall: Equations in Factored Form Where are the zeros/ x‐intercepts? Equation y = (x ‐ 4)(x + 2) y = x (x ‐ 5) y = (x + 3)2 Roots Sketch Recall: The zeros/x‐intercepts/roots are the values of x that cause the function, y, to equal zero. If (a)(b) = 0, either a = 0 or b = 0. Ex. 1 What are the zeros for each quadratic function? When does this When does this When does this When does this When does this factor =0? factor =0? factor =0? factor =0? factor =0? y = (2x + 1)(3x ‐ 2) y = x (5x ‐ 2) y = (2x + 7)2 5.2 Solving From Factored Form FULL.notebook November 28, 2022 Ex. 2 Solve. (find the roots/x‐intercepts/zeros/solutions) a) (x ‐ 5)(2x + 3) = 0 b) x (3x ‐ 5) = 0 c) (x ‐ 3)(x + 3) = 0 d) (5x ‐ 1)2= 0 e) (3x ‐ 2)(2x + 7) = 0 f) 6x(3x + 4) = 0 g) (2x + 5)(3x + 7) = 0 h) ‐x(5x ‐1) = 0. Ex. 3 Determine a quadratic equation in FACTORED form having these roots. a) 3, ‐2 b) 0, 5 c) 4, ‐4 d) only one root at ‐7 e) ¾, ‐½ f) Standard Form no brackets y = ax2 + bx + c quadratic function starts with x2 term constant term is at the end 0 = ax2 + bx + c quadratic equation all like terms are combined Ex. 4 Determine a quadratic equation in STANDARD form having these roots. Assume that a=1 Change from factored form to a) 5, 1 b) standard from by MULTIPLYING.
