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U really need help. i have a test coming up

U really need help. i have a test coming up-example-1
User Hasanuzzaman
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1 Answer

17 votes
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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

User DkAngelito
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