"the equation of a parabola in "color(blue)"vertex form"the equation of a parabola in 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"
"given the parabola in "color(blue)"standard form"
•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0
"then the x-coordinate of the vertex is"
•color(white)(x)x_(color(red)"vertex")=-b/(2a)
7y=4x^2+2x-3larrcolor(blue)"divide all terms by 7"
rArry=4/7x^2+2/7x-3/7larrcolor(blue)"in standard form"
"with "a=4/7,b=2/7
rArrx_(color(red)"vertex")=-(2/7)/(8/7)=-1/4
"substitute this value into equation for y-coordinate"
y_(color(red)"vertex")=4/7(-1/4)^2+2/7(-1/4)-3/7
color(white)(xxxx)=1/28-2/28-12/28=-13/28
"here "a=4/7" and "(h,k)=(1/4,-13/28)
rArry=4/7(x+1/4)^2-13/28larrcolor(red)"in vertex form"
