Question

How do you find the vertex and axis of symmetry, and then graph the parabola given by: `y = –x^2 + 4x + 2`?

Answer 1

Vertex is `(2,6)`
Axis of symmetry `x=2`

Explanation:

Given -

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

Find Vertex

`x=(-b)/(2a)=(-4)/(2 xx -1) =(-4)/(-2)=2`

At `x=2`

`y =-(2^2)+4(2)+2`
`y =-4+8+2=-4+10=6`

Vertex is `(2,6)`
Axis of symmetry `x=2`
Take two values on either side of `x=2`. Find the corresponding `y` values. Plot them in a graph sheet. Join them with a smooth curve.
x y

0 2
1 5
2 6
3 5
4 2

graph{-x^2+4x+2 [-14.23, 14.24, -7.12, 7.11]}