What is the vertex form of #y= -5x^2+x-2 #?
1 Answer
Sep 11, 2017
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 multiplier.
#"for a parabola in standard form "y=ax^2+bx+c#
#"the x-coordinate of the vertex is " x_(color(red)"vertex")=-b/(2a)#
#y=-5x^2+x-2" is in standard form"#
#"with "a=-5,b=1,c=-2#
#rArrx_(color(red)"vertex")=-1/(-10)=1/10#
#"substitute this value into the equation for y"#
#y_(color(red)"vertex")=-5(1/10)^2+1/10-2=-39/20#
#"here "(h,k)=(1/10,-39/20)" and "a=-5#
#rArry=-5(x-1/10)^2-39/20larrcolor(red)" in vertex form"#
