Question

What is the vertex of `y=x^2-3x-21`?

Answer 1

`"vertex "=(3/2,-93/4)`

Explanation:

`"given a parabola in "color(blue)"standard form ";ax^2+bx+c`

`"then the x-coordinate of the vertex is"`

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

`x^2-3x-21" is in standard form"`

`"with "a=1,b=-3" and "c=-21`

`x_("vertex")=-(-3)/2=3/2`

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

`y_("vertex")=(3/2)^2-3(3/2)-21=-93/4`

`color(magenta)"vertex "=(3/2,-93/4)`