Question

Find an equation l is standard form of the parabola passing through the points (-2,9), (-4,5), (1,0)​

Answer 1

Answer:

y =  -x^2 - 4x + 5.

Step-by-step explanation:

As it passes through the point (1, 0) it must have one zero of value x = 1 so it has a factor (x - 1).

so y = a(x - 1)(x - b) where a and b are constants.,

Now we substitute  the points (-2, 9) and (-4, 5) into this equation:

9 = a(-2 - 1)(-2 - b)

9 = a(-3)(-2- b)

9 =  6a + 3ab -----------(1)

5 = a(-4 - 1)(-4 - b)

5 = -5a(-4 - b)

5 =  20a + 5ab............(2)

Multiply (1) by 5 and (2) by 3

45 = 30x + 15ab

15 = 60a + 15ab

Subtracting these 2 equations:

30 = -30a

a = -1.

Substituting a = -1 in  equation (1):

9 = 6(-1) + 3(-1)b

3b = -6 - 9

b = -15/3

b = -5.

So the equation is y =  -(x - 1)(x + 5).

In standard form

y = -(x^2 + 4x - 5)

y =  -x^2 - 4x + 5.