i'm totally stumped on this problem!!?

Question

i need to find the equation for this chart


x, y
-3, -8
-2, 2
-1, 8
0, 10
1, 8
2, 2
3, -8

thank you!

Answer 1

You can tell it's an upside down parabola reaching its maximum at (0,10)

So it's y = ax^2 + bx + 10 where a is negative.

The function drops 2 on either side so try y = -2x^2 + 10

If this doesn't work insert an x term so that it does.

To solve algebraically you'd have to set up two equations using any 2 points: (here I use (1,8) and (2,2)

a(1)^2 + b(1) + 10 = 8
a(2^2) + b(2) + 10 = 2

a + b = -2
4a + 2b = -8

Then solve them

Answer 2

y = -2x^2 +10

Answer 3

y = 10 - 2x^2