How do you write the vertex form equation of the parabola #y = x^2 + 8x - 1#?

1 Answer
Jun 1, 2017

#y=(x+4)^2-17#

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.

#"for the standard form of a parabola " y=ax^2+bx+c#

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

#"here " a=1,b=8,c=-1#

#rArrx_(color(red)"vertex")=-8/2=-4#

#"for the y-coordinate, substitute this value into"#
#"the equation"#

#rArry_(color(red)"vertex")=(-4)^2+8(-4)-1=-17#

#rArrcolor(magenta)"vertex "=(-4,-17)#

#rArry=(x+4)^2-17larrcolor(red)" in vertex form"#