# What is the axis of symmetry and vertex for the graph #y=-x^2+6x-4#?

##### 1 Answer

Aug 15, 2017

#### Explanation:

#"given the equation of a parabola in standard form"#

#•color(white)(x)y=ax^2+bx+c color(white)(x);x!=0#

#"the x-coordinate of the vertex and axis of symmetry is"#

#x_(color(red)"vertex")=-b/(2a)#

#y=-x^2+6x-4" is in standard form"#

#"with "a=-1,b=6,c=-4#

#rArrx_(color(red)"vertex")=-6/(-2)=3#

#"substitute this value into the equation for the"#

#"corresponding y-coordinate"#

#rArry_(color(red)"vertex")=-9+18-4=5#

#rArrcolor(magenta)"vertex "=(3,5)#

#"equation of axis of symmetry is "x=3#

graph{(y+x^2-6x+4)(y-1000x+3000)=0 [-10, 10, -5, 5]}