The parabola in the figure below has an equation of the form y = ax^2 + bx - 4.

Find the equation of the parabola

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 )

8/k

step-by-step explanation: