URGENT:parabola equations

[Goistein]

Find the equations of the parabolas with the following three parts.(3 parts)

a. (0,4), (-1, 2), (3, -2)
b. (2,7), (5, 4), (3, 2)
c. (0, 1), (-4, 0), (-5, -4)

This is due tommorow. You don't have to show work.

 

[skeeter]

how about I do one and you do the other two the same way?

a parabola has an equation y = ax² + bx + c

you are given three points in (x,y) form ... a. (0,4), (-1, 2), (3, -2)

make three equations using the x and y values from each point ...

4 = a(0)² + b(0) + c
2 = a(-1)² + b(-1) + c
-2 = a(3)² + b(3) + c

the first equation tells you c = 4 ... update the other two equations

2 = a - b + 4 ... so a - b = -2
-2 = 9a + 3b + 4 ... 9a + 3b = -6

since a - b = -2, a = b - 2 ... substitute (b - 2) for a in the 2nd equation

9(b - 2) + 3b = -6
solve for b ...
9b - 18 + 3b = -6
12b = 12
b = 1

since a = b - 2, a = 1 - 2 = -1

so ... you have a = -1, b = 1, and c = 4
the parabola's equation is ...
y = -x² + x + 4

check your answer by evaluating the equation at each x-value ... you should get the corresponding y-value.

good luck with the other two.

 

[Goistein]

I can do this but it takes too long. I need to do my usamts. Hopefully you know what that is?

 

[Mrspi]

I can do this but it takes too long. I need to do my usamts. Hopefully you know what that is?

Skeeter worked through one of your problems completely. You can't do the others the same way? It takes too long??

Sometimes there is no "quick and easy" way to do a problem. If you're thinking we'll do your work for you, I think you're mistaken about what our purpose is here.