Determine a Quadratic Equation Given Its Roots - McGraw-Hill ...

Method 2: Use a Graphing Calculator1. Use the information given to identify three points and draw a sketch.Enter the three data points into a graphing calculator using L1 and L2.Tools• graphing calculator2. Use quadratic regression to find the equation of the quadraticfunction in the form y = ax 2 bx c.3. Enter the function for Y1 and graph the equation to verify.4. a) The intercept form of a quadratic function is y 5 a(x r)(x s),where r and s are the x-intercepts. Write this form of the function,using the same value of a as found in step 2 and the data fromthe original problem. Enter this form of the function as Y2 on thegraphing calculator, choose a different thickness for the new line,and graph this line.b) What do you notice occurs on the display of the graphingcalculator as the second parabola is graphed?5. Reflect Can you determine the equation of a quadratic functiongiven its zeros? If so, describe how. If not, explain why not.Example 1Find the Equation of a Family of Quadratic FunctionsFind the equation, in factored form, for a family of quadratic functionswith the given x-intercepts. Sketch each family, showing at least threemembers.a) 4 and 2b) 0 and 5c) 3 and 3d) 6 is the only x-interceptConnectionsFunctions that havea common propertyare called a family. Ingrade 9, you workedwith families of linearfunctions that have thesame slope: they areparallel lines.Solutiona) Since x 5 4 and x 5 2 areroots of the equation, x 4and x 2 are factors of the function.The equation for this family isf (x) 5 a(x 4)(x 2).y42f(x) = (x — 4)(x — 2)0 2 4 6 8 10 x—2—4f(x) = 2(x — 4)(x — 2)f(x) = 4(x — 4)(x — 2)1.6 Determine a Quadratic Equation Given Its Roots • MHR 53