Question

How do you graph `y=-x^2+2x+4`?

Answer 1

Substitute values for `x`, solve for `y`, draw a graph through the points. Be sure to use positive and negative values for `x`.

Explanation:

`y=-x^2+2x+4`

Point A: `(-3,-11)`

`x=-3`
`y=-(3^2)+(2*-3)+4=-9-6+4=-11`

Point B: `(-1,1)`

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

Point C: `(0,4)`

`x=0`
`y=-(0^2)+(2*0)+4=4`

Point D: `(1,5)`

`x=1`
`y=-(1^2)+(2*1)+4=-1+2+4=5`

Point E: `(3,1)`

`x=3`
`y=-(3^2)+(2*3)+4=-9+6+4=1`

Plot the points and draw a graph through the points. It will be a parabola.

graph{y=-x^2+2x+4 [-11.72, 8.28, -3.77, 6.23]}