Tutor profile: Ben S.
Determine the vertex of the parabola where y = 2x^2 - 8x + 7
We know that x = -b/2a -> (8/4) = 2. --> y=2(2^2)-8(2)+7 = -1
Solve for X: 6/x = 12/24
There are a couple ways to solve this. The most direct approach would be to cross multiply the numbers, in this case: multiply 12 and x, and multiply 24 and 6. 24*6 = 144. -> 144 = 12x. x = 12
Factor the following: x^2 - x - 12 = 0
We start off by looking at the first and last terms, seeing the factors. For x^2, the only possible factors are 1, or x and x. For -12, we can have a combination of 1 and 12, 2 and 6, or 3 and 4. We see that the middle term is -1, meaning the difference between the factors are off by 1, in this case, 3 and 4. Because it's negative, there's more weight on the negative than the positive number, so we come up with (x-4)(x+3). We use FOIL to get x^2 + 3x - 4x - 12 = x^2 - x - 12!
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