Question

what is the equation in standard form of parabola that contains the following points
(-2-20) (0,-4) (4,-20)

Answer 1

The standard form of a parabola is y = ax^2 + bx + c. We can substitute the given points into this equation to find a, b, and c.

For point (-2, -20):

-20 = a(-2)^2 + b(-2) + c,
-20 = 4a - 2b + c ------ (1).

For point (0, -4):

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

For point (4, -20):

-20 = a(4)^2 + b(4) + c,
-20 = 16a + 4b + c ------- (3).

We now have a system of three equations. From equation (2) we know that c = -4. Substituting c = -4 into equations (1) and (3) we get:

-20 = 4a - 2b - 4,
16 = 4a - 2b ------ (4),

-20 = 16a + 4b - 4,
-16 = 16a + 4b ------- (5).

Subtracting equation (5) from equation (4) gives:

32 = -20a,
a = -32/20 = -8/5 = -1.6.

Substituting a = -1.6 into equation (4) gives:

16 = -6.4 - 2b,
20 = 2b,
b = 10.

The equation of the parabola is therefore y = -1.6x^2 + 10x - 4.