Question

Find the standard equation and graph of a parabola that matches the given set of characteristics. focus (0, 7); vertex (0, 5)

Answer 1

The focus and vertex lie on the y axis, which means that the parabola is vertical and facing up. Hence the equation of the parabola to be used here is (x-h)^2 = 4a(y-k)

Here h and k are the x and y coordinates of the vertex (0, 5). Further, distance between the focus and vertex is 7 - 5 = 2, which means a = 2

Plugin the values of h, k and a into the equation above to get the equation of the parabola. Rewrite it in standard form by solving for y.

Answer 2

I don't know how to do anything like that. That's why I came on here.... it's for an online course....so there's no work just a, b, c, or d.

Answer 3

Kind of. I just want the answer. I know that people on here are like "You should learn it" but I don't have to, or want to. So if someone could please tell me what the answer is, that would be great.

Answer 4

Okay then just try to understand the basics: We find out the values of certain variables and plug them in the formula (x-h)^2 = 4a(y-k)

We find out the value of h and k from the question itself which states that the vertex coordinates are (0, 5). Hence h = 0 and k = 5.

Then we find out the value of 'a' by calculating the distance between the vertex and the focus. The distance between (0, 5) and (0, 7) is 7 - 5 = 2, hence a = 2.

Then plug in the values of h, k and a into the equation to get

(x - 0)^2 = 4*2(y - 5)

So you get

x^2 = 8y - 40

solve the equation for y to get it in standard form

8y = x^2 + 40

y = x^2/8 + 5

Answer 5

THANK YOU!!