"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=x^2+2(-2)x+4-4-2y=x2+2(−2)x+4−4−2
y=(x-2)^2-6larrcolor(red)"in vertex form"y=(x−2)2−6←in vertex form
color(magenta)"vertex "=(2,-6)vertex =(2,−6)
"to obtain the x-intercepts let y = 0"to obtain the x-intercepts let y = 0
(x-2)^2-6=0(x−2)2−6=0
(x-2)^2=6(x−2)2=6
color(blue)"take the square root of both sides"take the square root of both sides
x-2=+-sqrt6larrcolor(blue)"note plus or minus"x−2=±√6←note plus or minus
"add 2 to both sides"add 2 to both sides
x=2+-sqrt6larrcolor(red)"exact values"x=2±√6←exact values
