Question

The equation y1=x2−4x represents Function 1. The graph of Function 1 is shown.The graph title is Function one. The x and y axes range from negative nine to nine in increments of one. A U-shaped graph is shown. It starts with an arrow at midway between negative one and negative two, nine, passes through two, negative four, and ends with an arrow at midway between five and six, nine.Function 2 is represented by the equation y2=x−6. Which values are solutions to y1=y2? Select each correct solution.

Answer 1

Given:

Function 1 is,

`y_1=x^2-4x`

Function 2 is,

`y_2=x-6`

To find:

The solutions when

`y_1=y_2`

Step-by-step explanation:

Equating equations 1 and 2 we get,

`\begin{gathered} x^2-4x=x-6 \\ x^2-5x+6=0 \\ x^2-3x-2x+6=0 \\ x(x-3)-2(x-3)=0 \\ (x-3)(x-2)=0 \\ x=2,3 \end{gathered}`

Therefore, the solutions are,

`x=2\text{ and }x=3`

Final answer:

The solutions are,

`x=2\text{ and }x=3`