What is the vertex and range of the graph

Vertex of g(x) = ( -4 , 4)

Range of g(x)  is  

Step-by-step explanation:

For the Vertex of g(x),

Vertex of the graph is also called the turning point of the graph, as we see the graph of g(x) we can see that the axis of symmetry is at x = -4 meaning that left side of the graph on x = -4 is a mirror reflection on the right side of the graph.

So the x-coordinate of the vertex is -4

Now for the y-coordinate,

y-coordinate of the vertex is where the axis of symmetry occurs so the axis of symmetry is at x = -4 if we trace where x = -4 leads us we can see that it leads to y = 4 so the vertex of g(x) is ( -4 , 4)

Now for the Range of g(x),

The range is the set of possible output values, which are shown on the y-axis. Here we can see that the maximum value of g(x) on the y-axis is 4 then the values on the y-axis decrease

For example

Maximum value is 4 then decreases from there like 4 , 3 , 2 , 1 , 0 , -1 , -2 .... and so on if we see the graph . So the max value is 4 so the range becomes ,

because the maximum value is 4 and then decreases so that is why we add the less than equal to sign.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet