What is the axis of symmetry and vertex for the graph #y = 3x^2 - 9x + 12#?

2 Answers
Jim G.
Jul 5, 2018

#x=3/2," vertex "=(3/2,21/4)#

Explanation:

#"given a quadratic in "color(blue)"standard form"#

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

#"then the axis of symmetry which is also the x-coordinate"#
#"of the vertex is"#

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

#y=3x^2-9x+12" is in standard form"#

#"with "a=3,b=-9" and "c=12#

#x_("vertex")=-(-9)/6=3/2#

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

#y_("vertex")=3(3/2)^2-9(3/2)+12=21/4#

#color(magenta)"vertex "=(3/2,21/4)#

#"equation of axis of symmetry is "x=3/2#
graph{(y-3x^2+9x-12)((x-3/2)^2+(y-21/4)^2-0.04)=0 [-14.24, 14.24, -7.12, 7.12]}

Harish Chandra Rajpoot
Jul 5, 2018

#x=3/2# & #(3/2, 21/4)#

Explanation:

Given equation:

#y=3x^2-9x+12#

#y=3(x^2-3x)+12#

#y=3(x^2-3x+9/4)-27/4+12#

#y=3(x-3/2)^2+21/4#

#(x-3/2)^2=1/3(y-21/4)#

The above equation shows an upward parabola: #X^2=4AY# which has

Axis of symmetry : #X=0\implies x-3/2=0#

#x=3/2#

Vertex: #(X=0, Y=0)\equiv (x-3/2=0, y-21/4=0)#

#(3/2, 21/4)#

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