Find the X intercepts of the parabola with vertex (1,405) and Y intercept (0,400)

Step-by-step explanation:

The standard form of a parabola is

If we know the y intercept is (0, 400), that means that when x = 0, y = 400. That allows us to begin by finding c:

and c = 400.

Now to find a and b. Using the fact that the vertex is (1, 405), we know that h is 1 and k is 405. If

and h = 1, then

and

2a = -b so

b = -2a.  Save that for a minute or two.

If

and k = 405, then

and

and

405 = 400 - 4a and

5 = -4a so

We will use that a value now to find the value of b.  If b = -2a, then

and

Writing our parabolic equation now:

Finding the x-intercepts is just another way of saying "factor this quadratic" so we will begin that by setting the quadratic equal to 0:

and who hates all those fractions more than I do? Probably nobody, so we are going to get rid of them by multiplying everything by 4 to get

Assuming you can throw that into the quadratic formula to solve for the 2 values of x where y = 0, you'll find that the x-intercepts are

x = -16.91647287 and 18.91647287

step-by-step explanation: