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.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

687.09 dollars       happy now

step-by-step explanation: 6870

1857 times .63 equals 1169.91 subtract that from 1857 you get 687.09