Question

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

Answer 1

Answer:

Step-by-step explanation:

The standard form of a parabola is

$y=ax^2+bx+c$

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:

$400=a(0)^2+b(0)+c$ 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

$h=\frac{-b}{2a}$ and h = 1, then

$1=\frac{-b}{2a}$ and

2a = -b so

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

If

$k=c-\frac{b^2}{4a}$ and k = 405, then

$405=400-\frac{(-2a)^2}{4a}$ and

$405=400-\frac{4a^2}{4a}$ and

405 = 400 - 4a and

5 = -4a so

$a=-\frac{5}{4}$

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

$b=-2(-\frac{5}{4})$ and

$b=\frac{10}{4}$

Writing our parabolic equation now:

$y=-\frac{5}{4}x^2+\frac{10}{4}x+400$

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:

$0=-\frac{5}{4}x^2+\frac{10}{4}x+400$ 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

$-5x^2+10x+1600=0$ 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

Answer 2

Answer: ( -8,0),(10,0)

Step-by-step explanation: