OK, to find the equation for the line tangent to Y equal -2 -, 4 X squared at 4:00, -66, we're going to use the formula F of X + H -, F of X all divided by H So we know that the X has given us 4, so we're going to stick in 4 + H every time we see our unknown. So we get -2 -, 4 the quantity 4 + H quantity squared minus our F of X. And we know our F of X is -66 because it's given us the 4, -66. We're going to divide all that by H We're going to then foil out the 4 + H ^2. So the 16 + 8 H plus H ^2 distributing the -4 we get -2 -, 64 -, 32 H minus four H ^2 + 66. The -2 negative 64 and +66 are going to cancel. So that gives us -32 H minus four H ^2 / H. Then the HS will cancel, giving us -32 -, 4 H. Now what we need to think about is as H gets smaller and smaller and smaller because we want it tangent, the slope would actually just be -32 because that -4 * 0 would turn into 0. Using point slope form, we'd have Y minus the given Y of -66 equaling the slope of -32 times the quantity X -, 4. Distribute that out so we get it in Y equal form and we end up with Y equal -30 two X + 62.