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

##### 2 Answers

#### 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]}

#### Explanation:

Given equation:

The above equation shows an upward parabola:

**Axis of symmetry** :

**Vertex**: