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F(x)=-2^2-4x+1. write the equation in the form f(x)=a(x-h)^2+k. then give the vertex of its graph.

User Berke
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Answer: The vertex of the parabola is at the point (-1, 3).

User Latika
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Answer:

Starting with the given function:

f(x) = -2x^2 - 4x + 1

To write this in the form f(x) = a(x-h)^2 + k, we need to complete the square. We can do this by adding and subtracting a constant term that will make the expression a perfect square trinomial.

f(x) = -2(x^2 + 2x) + 1

f(x) = -2(x^2 + 2x + 1) + 2 + 1 (adding and subtracting 1)

f(x) = -2(x + 1)^2 + 3

Therefore, the equation in the form f(x) = a(x-h)^2 + k is f(x) = -2(x + 1)^2 + 3, where a = -2, h = -1, and k = 3.

The vertex of the parabola is at the point (-1, 3).

User Kovalsky Dmitryi
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