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Coordinates of the vertex, domain and range, the maximum or minimum value y=-4x^2?

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Without graphing each function, direction of the opening, coordinates of the vertex, domain and range, the maximum or minimum value y=-4x^2?

asked Feb 7, 2015 in CALCULUS by anonymous

1 Answer

0 votes

Step 1:

The parabola equation is image.

Compare with standard form of parabola image.

image

Since image, the parabola opens down and has maximum value.

Vertex is the maximum point of this function.

Step 2:

Find the vertex.

image-coordinate of vertex is image.

image

image

Substitute the value image in image.

image

image

Vertex image.

Step 3:

We know that domain of the function is all possible image values and range is all possible image values.

Parabola domain is all real numbers.

In the maximum point image, so the graph of parabola cannot be upper than 0.

Thus the range of function image.

Range set is image.

Solution:

image opens down.

Vertex image.

Domain is all real numbers.

Range image

Maximum value image.

answered Feb 9, 2015 by david Expert

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