Question

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.

Answer 1

Answer:

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

Step-by-step explanation:

Given : The quadratic functions $y = -2x^2$ and $y = -2x^2 + 4$

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

Solution :

Let, $y_1= -2x^2$

and  $y_2= -2x^2 + 4$

Now, we plot these two equations.

The graph of $y_1= -2x^2$  is shown with green line with vertex(0,0)

The graph of $y_2= -2x^2 + 4$  is shown with violet line with vertex(0,4)

We have seen in the graph that the graph of $y_2$ is shifted 4 unit upward with the graph of $y_1$

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.                

Answer 2

Answer:

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.