Find the vertex, axis of symmetry, y intercept of each parabola. State the number of x intercepts. Then sketch the graph of each function. f(x)=2(x-4)^2+4

Vertex: , Axis of symmetry: , no x-Intercepts, y-Intercepts: . The graph is represented in the image attached below.

Step-by-step explanation:

The equation of the parabola in vertex form and whose axis of symmetry is vertical is described by this formula:

(1)

Where:

- Independent variable.

- Dependent variable.

- Vertex constant.

- Coordinates of the vertex.

By direct comparison, we find the following information:

, ,

Vertex

The vertex is a point of the parabola so that .

If we know that and , then the coordinates of the vertex are .

Axis of symmetry

The axis of symmetry is a line of the form .

If we know that , then the axis of symmetry is .

To find the x and y intercepts, we need to transform the equation of the parabola into its standards, which is a second grade polynomial:

If we know that , and , then the equation of the parabola in standard form is:

x-Intercepts

The x-intercepts of the polynomial (if exist) can be found by the Quadratic Formula:

As both roots are conjugated complex numbers, there are no x-intercepts.

y-Intercepts

The y-intercept (if exists) can be found by evaluating the polynomial at :

The y-intercept is .

Lastly, we proceed to plot the function by using graphing tools.

look a the sides they are perpendicular

it would be:

c.parallelogram.