Question

What equation does the graph of system of equations solve?

a. x2 − 2x − 1 = −x2 + 3
b. x2 − 2x + 3 = x2 − x + 1
c. −x2 − 2x + 2 = 2x2 − x − 2
d. −x2 − 2x + 1 = 2x2 − x + 2

Ten points!

Answer 1

The required Equation is
`x^2-2x-1=-x^2+3`

Explanation:

Given : The graph of two equations intersecting each other at (-1,2) and (2,-1).

To find : What equation does the graph of system of equations solve?

Solution :

To find the equations we have to put the points if the equation satisfied then it is the required equation.

a)
`x^2-2x-1=-x^2+3`

Let
`y_1=x^2-2x-1` and
`y_2=-x^2+3`

Put (-1,2)

`2=(-1)^2-2(-1)-1` and
`2=-(-1)^2+3`

`2=1+2-1` and
`2=-1+3`

`2=2` and
`2=2`

Put (2,-1)

`-1=(2)^2-2(2)-1` and
`-1=-(2)^2+3`

`-1=4-4-1` and
`-1=-4+3`

`-1=-1` and
`-1=-1`

As the equation satisfying the points.

Therefore, The required Equations i
`x^2-2x-1=-x^2+3`

Answer 2

a. x^2 − 2x − 1 = −x^2 + 3

Explanation:

The red curve in the figure is described by 3-x^2. The only answer choice that includes that expression is choice a.

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The red curve is your basic y=x^2 curve reflected across the x-axis (y=-x^2) and shifted up 3 (y=-x^2+3).

Both curves go through the point that is 1 over and 1 up (or down) from the vertex, so the vertical scale factor is 1. That is, any choice with 2x^2 in it will not be an answer.