Determine the equation for the parabola graphed below.

We can see that (0, 6), (1, -1), and (-3, -1) are points of the parabola. 

The standard equation of a parabola is .

Substituting x=0, and y=6 we get: 6=0+0+c, which means that c=6.

So, we rewrite the equation as .

Substituting (1, -1), and (-3, -1) in the equation we get the following equations in terms of a and b:

i)

-1=a(1)^2+b(1)+6
-1=a+b+6
a+b=-7

ii)

-1=a(-3)^2+b(-3)+6
-1=9a-3b+6
9a-3b=-7

Thus, we have the system:

i)  a+b=-7
ii) 9a-3b=-7

writing b=-a-7 from (i), and substituting into (ii) we have:

9a-3(-a-7)=-7

9a+3a+21=-7

12a=-28

a=-28/12=-7/3

Thus, b=-a-7=7/3  -7  =7/3  -21/3 = -14/3

It’s 24.6 after you round to the nearest tenths the answer should be 25.0