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

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

when multiplying or dividing by a negative on both sides you have to flip the inequality sign. this rule only applies to multiplying or dividing by a negative number in inequality equations. this rule is really important.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice