Question

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

Answer 1

`x=-7/4" and "(-7/4,-217/8)`

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`