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.

1)is not similar since corresponding sides are not in the same ratio

2)are similar since corresponding sides are in the same ratio and corresponding angles are equal

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step-by-step explanation: ; )