The vertex form of a quadratic function is expressed as
f(x) = a(x - h)^2 + k
The parabola opens downwards. it means that a would be negative
The maximum value, k = - 2
The coordinates of the vertex are (- 3, - 2)
h = - 3, k = - 2
We would substitute the parabola's vertex into the formula above. It becomes
f(x) = a(x - - 3)^2 + - 2
f(x) = a(x + 3)^2 - 2
Todetermine a, we would find another point on the parabola. This point is (- 1, - 5)
We would substitute this point into the equation. It becomes
- 5 = a(- 1 + 3)^2 - 2
- 5 = a*2^2 - 2
- 5 = 4a - 2
4a = - 5 + 2
4a = - 3
a = - 3/4
We would substitute the value of a into the equation. It becomes
y = - 3/4(x + 3)^2 - 2
Vertex = (- 3, - 2)
Additional point = (- 1, - 5)
a = - 3/4
equation or rule = y = - 3/4(x + 3)^2 - 2
f(-3) = - 3/4(- 3 + 3)^2 - 2
f(- 3) = 0 - 2 = - 2
f(1) = - 3/4(1 + 3)^2 - 2
f(1) = - 3/4 * 16 - 2 = - 12 - 2
f(1) = - 14
2f(- 3) + f(1) = 2 * - 2 + - 14
2f(- 3) + f(1) = - 4 - 14 = - 18