Question

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

Answer 1

Explained below

Explanation:

The given function is a quadratic function , which would represent a parabola. Hence it would be prudent to put it in the vertex form.

It would be y=`-(x^2 -2x) +3`

That is y = `-(x-1)^2 +4`

This shows that vertex is (1,4) and axis of symmetry is x=1. The parabola would open downwards because the coefficient of `x^2` is negative. y -intercept would be 3 and x intercepts would be -1 and 3. With all this information available, the parabola can be easily graphed.[For x intercepts put y=0 and factorise #-x^2 +2x-3=0]