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

Question

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

Answer 1

Step 1:

The parabola equation is .

Compare with standard form of parabola .

Since , the parabola opens down and has maximum value.

Vertex is the maximum point of this function.

Step 2:

Find the vertex.

-coordinate of vertex is .

Substitute the value in .

Vertex .

Step 3:

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

Parabola domain is all real numbers.

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

Thus the range of function .

Range set is .

Solution:

opens down.

Vertex .

Domain is all real numbers.

Range

Maximum value .