Question

Write a rule for a function with a parabolic graph that contains the x-intercepts (-20,0) and (40,0) and a maximum point whose y-coordinate is 30.

Answer 1

Explanation:

Since the x-intercepts are -20 and 40, the line of symmetry is x = (-20 + 40)/2 = 10.

Now we have y = a(x - 10)² + 30, where a is an unknown constant. We can find a by using an x-intercept point.

=> (0) = a[(40) - 10]² + 30

=> 900a + 30 = 0, a = -1/30.

Hence the rule is y = -(x - 10)²/30 + 30.