Question

Example 2

Assuming that the graph of y = x2 – 3x + 1 has been drawn, find the equation of the line which
should be drawn to solve the equation:
x² - 4x +3=0




Y is equals to x to the power of 2 -3x+1 It’s not 2x incase you don’t get it please help!!ʕ•ᴥ•ʔ

Answer 1

y=x-2

Explanation:

If you have drawn the graph of
`y = x^2 - 3x + 1`.

To determine the equation of the line which should be drawn to solve the equation: x² - 4x +3=0

Simply carry out the subtraction:
`x^2 - 3x + 1 -(x^2 - 4x +3)`

`\implies x^2 -3x + 1-x^2 + 4x -3 \\= x^2 - x^2+ 4x - 3x-3 + 1\\=x-2`

The equation of the line which should be drawn is: y=x-2

What this means is simply:

If

`y = x^2 - 3x + 1$ and $y=x-2,$ then:\\x^2 - 3x + 1=x-2\\x^2 - 3x + 1-x+2=0\\x^2 - 4x + 3=0`