Question

Which graph can be used to find the solution(s) to x^2 – 4x + 4 = 2x – 1 – x^2?

Answer 1

See explanantion

Explanation:

Consider the equation
`x^2-4x + 4 = 2x-1-x^2.` This equation consists of two parts:

• left part is defined by the function
  `y=x^2-4x+4;`
• right part is defined by the function
  `y=2x-1-x^2.`

Both these functions are quadratic and determine parabolas. The graph of the function

`y=x^2-4x+4=(x-2)^2`

is parabola tangent to x-axis at point (2,0) with branches going up. The graph of the function

`y=2x-1-x^2=-(x-1)^2`

is parabola tangent to x-axis at point (1,0) with branches going down (see diagram). As you can see from the diagram these two parabolas do not intersect, then there are no solutions.