Determine a Quadratic Equation Given Its Roots - McGraw-Hill ...
Determine a Quadratic Equation Given Its Roots - McGraw-Hill ...
Determine a Quadratic Equation Given Its Roots - McGraw-Hill ...
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Solutiona) Since 2 and 3 are zeros, then x 2 and x 3 are factors.f (x) 5 a(x 2)(x 3)Substitute the given point: f (0) 5 33 5 a(0 2)(0 3)3 5 6aa 5 1_2 The function, in factored form, is f (x) 5 1_ (x 2)(x 3).2In standard form: f (x) 5 1_2 (x2 x 6)5 1_2 x2 1_2 x 3Check by graphing the function using agraphing calculator.b) Since 2 is a double zero, the factor x 2 is repeated.f (x) 5 a(x 2) 2Substitute the point: f (3) 5 1010 5 a(3 2) 210 5 25aa 5 0.4The function, in factored form, isf (x) 5 0.4(x 2) 2 .In standard form:f (x) 5 0.4(x 2 4x 4)5 0.4x 2 1.6x 1.6____c) Since 3 5 and 3 5 are zeros, then____( x ( 3 5 ))and ( x ( 3 5 ))are factors.____f (x) 5 a( x ( 3 5 ))( x ( 3 5 ))____5 a( x 3 5 )( x 3 5 ) This is in the form (c — d)(c + d), where__5 ) 2 ]c = x — 3 and d = __5 .5 a [ (x 3) 2 ( 5 a(x 2 6x 9 5)5 a(x 2 6x 4)Substitute the point: f (2) 5 1212 5 a(2 2 6(2) 4)12 5 a(4)a 5 3The function, in factored form, isf (x) 5 3(x 2 6x 4).In standard form:f (x) 5 3(x 2 6x 4)5 3x 2 18x 12Simplify and solve for a.1.6 <strong>Determine</strong> a <strong>Quadratic</strong> <strong>Equation</strong> <strong>Given</strong> <strong>Its</strong> <strong>Roots</strong> • MHR 55
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