Graph the quadratic functions y = -2x^2 and y = -2x^2 + 4 on a seperate piece of paper. using those graphs, compare and contrast the shape and position of the graphs.

Shape is parabolic and there is translation of 4 unit upward.

Step-by-step explanation:

Given : The quadratic functions and

To find : Using those graphs, compare and contrast the shape and position of the graphs?

Solution :

Let,

and  

Now, we plot these two equations.

The graph of  is shown with green line with vertex(0,0)

The graph of  is shown with violet line with vertex(0,4)

We have seen in the graph that the graph of is shifted 4 unit upward with the graph of

Transformation to upward,

f(x)→f(x)+b , the graph of f(x) is shifted upward by b unit.

The shape of both the graph is parabolic but the position is different.

There is a 4 unit upward translation.

Refer the attached graph below.                

both the graph has same shape but graph of y = -2x²+4 would shift 4 unit up.

Step-by-step explanation:

Given : y = -2x²   and y = -2x²+4.

To find  : Using those graphs, compare and contrast the shape and position of the graphs.

Solution : We have given that  y = -2x²   and y = -2x²+4.

For y = -2x²  

This is a quadratic equation  we will get a parabolic graph with y intercept 0

Vertex (0,0).

For y = -2x²+4

This is also a quadratic function , we will get parabolic graph with y intercept 4.

Graph of y = -2x²+4  would shift 4 unit up with y = -2x².

Therefore, both the graph has same shape but graph of y = -2x²+4 would shift 4 unit up.

step-by-step explanation: