What are the coordinates of the vertex of the parabola with the equation y = x + 2x - 3?

The coordinates of the vertex are (-1,-4).

Step-by-step explanation:

Equation of the Quadratic Function

The vertex form of the quadratic function has the following equation:

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.

We are given the function:

We must transform the equation above by completing squares:

The first two terms can be completed to be the square of a binomial. Recall the identity:

Thus if we add and subtract 1:

Operating:

The trinomial in parentheses is a perfect square:

Adding 4:

Comparing with the vertex form of the quadratic function, we have the vertex (-1,-4).

The coordinates of the vertex are (-1,-4).

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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