"given the parabola in standard form "ax^2+bx+cgiven the parabola in standard form ax2+bx+c
"the x-coordinate of the vertex is"the x-coordinate of the vertex is
x_(color(red)"vertex")=-b/(2a)xvertex=−b2a
2x^2+8x+13" is in standard form"2x2+8x+13 is in standard form
"with "a=2,b=8,c=13with a=2,b=8,c=13
rArrx_(color(red)"vertex")=-8/4=-2⇒xvertex=−84=−2
"substitute this value into the equation for y-coordinate"substitute this value into the equation for y-coordinate
rArry_(color(red)"vertex")=2(-2)^2+8(-2)+13=5⇒yvertex=2(−2)2+8(−2)+13=5
rArrcolor(magenta)"vertex "=(-2,5)⇒vertex =(−2,5)
"the equation of the parabola in "color(blue)"vertex form"the equation of the parabola in vertex form is.
•color(white)(x)y=a(x-h)^2+k∙xy=a(x−h)2+k
"where "(h,k)" are the coordinates of the vertex and a"where (h,k) are the coordinates of the vertex and a
"is a constant"is a constant
"here "a=2" and "(h,k)=(-2,5)here a=2 and (h,k)=(−2,5)
rArrg(x)=2(x+2)^2+5larrcolor(red)" in vertex form"⇒g(x)=2(x+2)2+5← in vertex form
