Question

How do you use the important points to sketch the graph of `y=x^2 - x - 12 = 0`?

Answer 1

Factorise first

Explanation:

If you factorise this equation, you will get:

`(x-4)(x+3)=0`

Putting each bracket equal to zero gives `x=4 or x=-3` as your x intercepts (where the graph crosses the x axis).

If you put `x=0`, this will give you your y intercept which in this case is `-12` (`0^2-0-12`).

As it's a quadratic (power of 2 in the equation) it will be a smooth, U-shaped curve going through the above points.