# How do you find the vertex and axis of symmetry for #f (x)= 2x² - 6x+ 3#?

##### 2 Answers

Given and equation of the form:

The equation for the axis of symmetry is:

The x coordinate for the vertex, h, is the same.

The y coordinate,

#### Explanation:

Given:

The equation for the axis of symmetry is:

The x coordinate of the vertex is the same:

The y coordinate of the vertex is:

The vertex is

#### Explanation:

#"the equation of a parabola in "color(blue)"vertex form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#

#"where " (h,k)" are the coordinates of the vertex"#

#"and a is a constant"#

#"to express f(x) in this form "color(blue)"complete the square"#

#f(x)=2(x^2-3xcolor(red)(+9/4)color(red)(-9/4))+3#

#color(white)(f(x))=2(x-3/2)^2-9/2+3#

#color(white)(f(x))=2(x-3/2)^2-3/2larrcolor(red)" in vertex form"#

#rArrcolor(magenta)"vertex" =(3/2,-3/2)#

#"since " a>0" then minimum "uuu#

#"the axis of symmetry passes through the vertex"# is vertical

#"with equation " x=3/2#

graph{(y-2x^2+6x-3)(y-1000x+1500)=0 [-10, 10, -5, 5]}