What is the equation of the parabola with a vertex of (2,-1) and passes through the point of (4,0)

Answer 1

If you're trying to find the equation of a parabola with vertex of (2, -1) and passes through the point (4,0), you'd want to find one that satisfies the said conditions of 4p(x-2)² = (y+1), where you're trying to solve for the unknown variable p given the point-vertex form of the parabola.

By plugging in x = 4 and y = 0 into the equation, you can find p = 1/16, and so the equation of the parabola is (1/4)*(x-2)² = (y+1), which satisfies the condition of vertex (2, -1) and passes through (4, 0).

Answer 2

When you know the vertex is located at (h,k), then the vertex form for a parabola looks like this:

y = a(x - h)² + k.

Given that the vertex is located at (2, -1), you now know that the function is starting to look like this:

y = a(x - 2)² - 1

The fact that the parabola passes through (4, 0) allows you to determine the value for a, i.e. when x = 4, y = 0.

0 = a(4 - 2)² -1

0 = 4a - 1

4a = 1

a = 1/4

So the vertex form for the equation of this parabola is:

y = (1/4) ( x - 2)² - 1

Visit this Desmos graph by selecting the URL, right-clicking and choosing "go to...".

desmos.com/calculator/om8harfyfl