# How do you find the axis of symmetry and vertex point of the function: #f(x) = -x^2 + 2x#?

##### 2 Answers

#### Explanation:

#"find the zeros by letting "f(x)=0#

#-x^2+2x=0#

#x(2-x)=0#

#x=0" and "x=2larrcolor(blue)"zeros"#

#"the x-coordinate of the vertex lies on the axis of symmetry"#

#"which is situated at the midpoint of the zeros"#

#"axis of symmetry is "x=(0+2)/2=1#

#"substitute this value into the equation for y-coordinate"#

#y_("vertex")=-1+2=1#

#color(magenta)"vertex "=(1,1)#

graph{-x^2+2x [-10, 10, -5, 5]}

**Vertex is at** **axis of symmetry is**

#### Explanation:

equation

here

Axis of symmetry is

graph{-x^2+2 x [-10, 10, -5, 5]} [Ans]