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

Key ConceptsThe zeros can be used to find the equation of a family of quadratic functions with thesame x-intercepts.To determine an individual quadratic function, you also need to be given one other pointon the function.Communicate Your UnderstandingC1Outline the steps needed to find the equation of a quadratic function given the x-interceptsand one other point on the function.C2C3You are given an equation for a family of quadratic functions with the same x-intercepts.Rita says, “The vertex is the only point that will not allow you to determine the exactequation, as it is at the centre of the function, and more than one function can be found.”Ronnie claims, “The vertex is as good as any other point in finding the exact function.”Who is correct? Explain.Mona has decided that if she is given a fraction such as ​1_ ​as one of the x-intercepts,2she can use the binomial (2x 1) instead of ​ ( x ​ 1_2 ​ ) ​and get the same quadratic function.Is she correct? Explain.A PractiseFor help with questions 1 and 2, refer toExample 1.1. Determine the equation, in factored form,of a family of quadratic functions witheach pair of roots. Sketch a graph to showfour graphs in each family.a) x 5 3 and x 5 6b) x 5 1 and x 5 1c) x 5 3 and x 5 42. Express each equation in question 1 instandard form.For help with question 3 to 5, refer toExample 2.3. Find the equation of a quadratic functionthat has the given x-intercepts andcontains the given point. Express eachfunction in factored form. Graph eachfunction to check.a) 3 and 5, point (4, 3)b) 4 and 7, point (3, 12)c) 0 and ​ 2_ ​, point (1, 5)34. Write each function in question 3 instandard form.5. Find the equation of the quadratic functionthat has the given zeros and contains thegiven point. Express each function instandard form. Graph each function tocheck.___a) 1 ​ 11__​, point (4, 6)b) 2 ​ __7 ​, point (1, 2)c) 5 ​ 2 ​, point (2, 14)6. Find the equation of the quadratic functionthat has the given zeros and contains thegiven point. Express each function invertex form. Graph each function to check.a) 3 and 1, point (1, 2)b) 1 and 2, point (0, 4)c) 3 and 5, point (1, 4)1.6 Determine a Quadratic Equation Given Its Roots • MHR 57