What is the equation, in standard form, of a parabola that contains the following points?

(-2,-20),(0,-4),(4,-20)

1- y=-2.5x^2+5x
2-y=-x^2+4x-4
3- y=-2x^2+4x-4
4-y=-2.25xx^2+4.5x-2

My answer is 3

looks good

Thank you

To find the equation of a parabola that passes through three given points, you can use the general form of the quadratic equation in standard form, which is:

y = ax^2 + bx + c

To find the values of a, b, and c, substitute the coordinates of each point into the equation and form a system of three equations. Let's do that for the given points:

Point 1: (-2, -20)
-20 = a(-2)^2 + b(-2) + c
-20 = 4a - 2b + c -- Equation (1)

Point 2: (0, -4)
-4 = a(0)^2 + b(0) + c
-4 = c -- Equation (2)

Point 3: (4, -20)
-20 = a(4)^2 + b(4) + c
-20 = 16a + 4b + c -- Equation (3)

Now, substitute c = -4 from Equation (2) into Equations (1) and (3):

-20 = 4a - 2b - 4 -- Equation (1')
-20 = 16a + 4b - 4 -- Equation (3')

Rearrange Equations (1') and (3') to solve for b:

4a - 2b = -16 -- Equation (1'')
16a + 4b = -16 -- Equation (3'')

Multiply Equation (1'') by 2 and Equation (3'') by 1, then add the equations to eliminate b:

8a - 4b = -32
16a + 4b = -16

24a = -48
a = -48/24
a = -2

Substitute the value of a = -2 into Equation (1'') to find b:

4(-2) - 2b = -16
-8 - 2b = -16
-2b = -16 + 8
-2b = -8
b = -8/-2
b = 4

Now that we have the values of a = -2, b = 4, and c = -4, we can write the equation of the parabola in standard form:

y = -2x^2 + 4x - 4

Therefore, the correct equation of the parabola is option 3: y = -2x^2 + 4x - 4.