Question

The diagram shows part of the graph of the quadratic function f(x) = a(x - h)(x - k) where h < k. Point P is the minimum point of the graph of the quadratic function.

what is a,h and k ?​

Answer 1

a = 3
h = 1
k = 5

Explanation:

• The graph and equation are for a parabola
  Equation is
  y = a(x - h)(x - k)

• The roots of the equation are where x = h and x =k. These correspond to the x-intercepts, where the graph crosses the x axis

• We have two values for x intercept:
  x = 1, x = 5

• Therefore we get
  y = a(x - 1)(x - 5)

• The y-intercept is 15 and this is where the graph crosses the -y-axis
  This will be the y-value at x = 0

• Plugging y = 15, x = 0 into y = a(x - 1)(x - 5)
  → 15 = a(0-1)(0-5)
  → 15 = a(-1)(-5)
  → 15 = 5a
  

• Therefore a = 15/5 = 3

• The equation of the parabola is
  y = 3(x - 1)(x - 5)