I have the points (0, 10) as the vertex, and (-10,0) and (10, 0)... How do I write that equation?

Question

I have a graph... and I picked the points... I neeed the equatoins for the graph...

It is a Quadratic Equation. A U-shaped graph.

Answer 1

Do you mean a parabola?

A normal parabola would be y = x^2 going through points (0, 0), (1, 1), (-1, 1).

Your parabola goes down because the vertex is higher, so make it y = -x^2. Now the points would be (0, 0), (1, -1), (-1, -1).

Next you need to offset it by 10 to get your vertex at (0, 10), so make it y = 10 - x^2. Now your points are (0, 10), (1, 9), (-1, 9)

Finally, two points are (-10, 0) and (10, 0). That would only work if x = 10 and x = -10 gave y = 0.

0 = 10 - a(x^2)
a(x^2) = 10
100a = 10
a = 1/10

So the final equation is y = 10 - (x^2)/10

Alternatively, you could write it as:
y = (-1/10)x^2 + 10

Answer 2

x^2=a(y-b) +c is a general equation
where (b,c) are the vertex
When (0,10) are vertex
x^2=a(y-10) +0...............i
Now put x=-10 and y =0
100=-10a
a=-(1/10).......................ii
x^2=(-1/10)(y-10)
or x^2= -y/10 +1