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

Answer 1

Abigail Allen

#x=3,(3,5)#

#"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]}

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Answer 2

Genesis Allen

The axis of symmetry for the graph of (y = -x^2 + 6x - 4) is (x = 3). The vertex is located at the point ((3, 5)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.