Question

How do you graph `f(x)=3-x^2` and identify the x intercepts, vertex?

Answer 1

Use the standard graph of `y=x^2` but upside down `(y=-x^2)` and then shift it up 3 units.

Explanation:

To find the `x` intercepts, make `f(x)=0` so `x^2=3`. Taking the square root of both sides gives `x=+-sqrt3`.

The vertex of the graph will be at `(0,3)` because the graph hasn't been translated left or right so is still symmetrical about the y-axis.