Question

The parabola in the figure below has an equation of the form

y = ax^2 + bx - 4.

Find the equation of the parabola

Answer 1

The trajectory of a projectile is parabolic and can be represented by the equation y = ax + bx². This expression is obtained by solving equations for x and y positions of the projectile and substituting the values into the equation for y.

Step-by-step explanation:

The trajectory of a projectile is parabolic and can be represented by the equation y = ax + bx², where a and b are constants. To obtain this expression, we can solve the equations x = Voxt for t and substitute it into the expression for y = Voyt - (1/2)gt². By doing this, we obtain an equation of the form y = ax + bx², where a and b are constants.

Answer 2

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 )