Answer:
y = - x² + 5x - 4
Step-by-step explanation:
Given that the zeros are x = 1 and x = 4 , then the corresponding factors are
(x - 1) and (x - 4) , then
y = a(x - 1)(x - 4) ← a is a multiplier
= a(x² - 5x + 4)
To find a substitute the coordinates of any other point on the parabola into the equation.
Using (2, 2), then
2 = a(4 - 10 + 4) = - 2a ( divide both sides by - 2 )
a = - 1
Thus
y = - (x² - 5x + 4) = - x² + 5x - 4 ( with a = - 1 and b = 5 )
