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

1 Answer
Oct 10, 2015

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]}