# What is the axis of symmetry and vertex for the graph #y= 2x^2+7x-21#?

##### 1 Answer

Feb 2, 2018

#### Explanation:

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

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

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

#"equation of the axis of symmetry is"#

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

#y=2x^2+7x-21" is in standard form"#

#"with "a=2,b=7" and "c=-21#

#rArrx_(color(red)"vertex")=-7/4#

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

#y_(color(red)"vertex")=2(-7/4)^2+7(-7/4)-21=-217/8#

#rArrcolor(magenta)"vertex "=(-7/4,-217/8)#

#"equation of axis of symmetry is "x=-7/4#