Sheri has been asked to find the quadratic equation of the graph below.

Question

Sheri has been asked to find the quadratic equation of the graph below. She can tell the solutions are x = 3 and x = 6. She also knows that the parabola opens up so the value of “a” would be positive. Because the axis of symmetry isn’t through a whole number she can’t figure out where to start. Help Sheri figure out the equation of the quadratic. Do this using algebra and give a reason with each step you need to take.

Answer 1

Solutions are 3 and 6                  Given

a > 0                                         Given

factors are (x-3) and (x-6)           Definition of Solution

 

0 = ±(x-3)(x-6)                           Zero Product Theorem

0 = ±(x² - 9x + 18)                     Binomial Multiplication

0 = x² - 9x + 18                           a > 0