Construct a quadratic function that has a vertex at (-2,3) and includes the value f(-1)=1.

f(x) = -2(x + 2)²+ 3

Step-by-step explanation:

Let the quadratic function be,

f(x) = a(x - h)² + k

Here, (h, k) is the vertex of the parabola

If (-2, 3) is the vertex of the parabola,

f(x) = a(x + 2)² + 3

And f(-1) = 1,

f(-1) = a(-1 + 2)² + 3

1 = a(1) + 3

a = 1 - 3

a = -2

Therefore, quadratic function is,

f(x) = -2(x + 2)²+ 3

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step-by-step explanation:

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