Amos J. answered • 12/11/18
Math and Physics
Hi Alice,
Have you solved systems of equations? For example:
Given
3a + 4b = 5
5a - 2b = 4
Find a and b.
(Answer: a = 1, b = 1/2)
The problem you've submitted is a system of equations problem. So, if you were able to solve the example I just gave, solving this parabola problem should be a snap.
Based on the way you asked your question, I can tell that you know that the equation for a parabola looks like this:
y = ax2 + bx + c
The problem gives you three points on that parabola. In other words, it gives you three different (x, y) pairs that will solve this equation. So, taking each point, you substitute the x- and y-coordinates into the equation and end up with three different equations involving the unknowns a, b, and c:
For the point (1, -2),
(-2) = a(1)2 + b(1) + c
Which I'll simplify and rearrange to look like:
a + b + c = -2
For the point (2, -2),
(-2) = a(2)2 + b(2) + c
Which simplifies to:
4a + 2b + c = -2
For the point (3, -4),
(-4) = a(3)2 + b(3) + c
Which simplifies to:
9a + 3b + c = -4
Now, you've got three equations with three unknowns (a, b, and c):
a + b + c = -2
4a + 2b + c = -2
9a + 3b + c = -4
From this point, there are a bunch of different ways you can solve the problem. I'll start you off with this:
Notice that the left-hand sides of the 1st and 2nd equations are both equal to -2, which means that those two left-hand sides are equal to each other, like so:
a + b + c = 4a + 2b + c
You can subtract c from both sides, then do a little bit of algebra to get an equation relating a to b:
a + b = 4a + 2b
-3a = b
That should help tremendously. Good luck with solving the rest of the problem, and if you run into a hiccup, let us know!
