# I need to find a tangent equation

#### IlanSherer

Hello I will be happy if you will help me please.

The equation is y = -1.2x + 180, and it looks like this: And I have to find a tangent equation at point (100, 60), it should look like this: I tried to find a tangent equation (The graph of a tangent equation should be as curved as a parabola) and I got this: It's good, but one problem - The parabola is below a straight line.
How do I find a tangent equation?

Thanks! #### skipjack

Forum Staff
Use y = a(x - 100)² - 1.2x + 180, where a > 0 (for example, a = 0.024).

(Using a = -0.018 would give your example.)

• IlanSherer

#### IlanSherer

Use y = a(x - 100)² - 1.2x + 180, where a > 0 (for example, a = 0.024).

(Using a = -0.018 would give your example.)
Thank you very much!
Can you tell/explain me please how did you find it?

#### skipjack

Forum Staff
You are seeking a quadratic in x (because the sought curve is a parabola), and the difference between that expression and the expression you gave for the line must also be a quadratic in x, and must correspond to a parabola that touches the x-axis at (100, 0), so its general form is a(x - 100)², where a is non-zero.

One can see that examples of the type you found have a < 0, and examples of the type you want have a > 0.

• IlanSherer