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How do you find the VERTEX of a parabola #f(x)= -3x^2-6x-7#?

Answer 1

Eva Adamson

Find vertex of f(x) = - 3x^2 - 6x - 7

Vertex (-1, -4)

Vertex x-coordinates: #x = (-b/2a) = 6/-6 = - 1# Vertex y-coordinate: y = f(-1) = -3 + 6 - 7 = - 4

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Answer 2

Jameson Allen

To find the vertex of a parabola in the form (f(x) = ax^2 + bx + c), where (a), (b), and (c) are constants, you can use the formula for the x-coordinate of the vertex:

[x_v = -\frac{b}{2a}]

Once you have the x-coordinate of the vertex, you can plug it back into the function to find the corresponding y-coordinate.

For the given parabola (f(x) = -3x^2 - 6x - 7):

[a = -3] [b = -6]

Plug these values into the formula:

[x_v = -\frac{-6}{2(-3)}] [x_v = -\frac{-6}{-6}] [x_v = 1]

Now, find the corresponding y-coordinate by substituting (x = 1) into the function:

[f(1) = -3(1)^2 - 6(1) - 7] [f(1) = -3 - 6 - 7] [f(1) = -16]

So, the vertex of the parabola (f(x) = -3x^2 - 6x - 7) is ((1, -16)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.