"the equation of a parabola in "color(blue)"vertex form"the equation of a 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 multiplier"is a multiplier
"to obtain this form "color(blue)"complete the square"to obtain this form complete the square
y=-6(x^2-5/6x-3)y=−6(x2−56x−3)
color(white)(y)=-6(x^2+2(-5/12)x+25/144-25/144-3)y=−6(x2+2(−512)x+25144−25144−3)
color(white)(y)=-6(x-5/12)+457/24larrcolor(blue)"in vertex form"y=−6(x−512)+45724←in vertex form
color(magenta)"vertex "=(5/12,457/24)vertex =(512,45724)
"to obtain the x-intercepts set y = 0"to obtain the x-intercepts set y = 0
-6(x-5/12)^2+457/24=0−6(x−512)2+45724=0
(x-5/12)^2=457/144(x−512)2=457144
color(blue)"take the square root of both sides"take the square root of both sides
x-5/12=+-sqrt(457/144)=+-sqrt457/12x−512=±√457144=±√45712
"add "5/12" to both sides"add 512 to both sides
x=5/12+-sqrt457/12larrcolor(red)"exact values"x=512±√45712←exact values
