Question

How do you graph `y=x^2-2x-3`?

Answer 1

Find and plot: the vertex, the `x` intercepts, the `y` intercept (and any other test values for `x` you like); then connect the dots.

Explanation:

`y=x^2-2x-3 =(x-3)(x+1)`

`y` intercept `= -3` `color(white)("XXXX")` (found by setting `x=0`)
`x` intercepts `=3` and `=-1` `color(white)("XXXX")`(from the factors)

vertex: `(x,y) = (1,-4)` `color(white)("XXXX")`(`x` by completing the square, `y` by substitution)
graph{x^2-2x-3 [-5.3, 7.19, -4.805, 1.435]}