#"express in standard form"#
#rArry=2x^2-12x+15#
#"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"#
#"to obtain this form use the method of "color(blue)"completing the square"#
#• " the coefficient of the "x^2" term must be 1"#
#rArr2(x^2-6x)+15#
#• " add/subtract "(1/2"coefficient of x-term")^2"to"#
#x^2-6x#
#2(x^2+2(-3)xcolor(red)(+9)color(red)(-9))+15#
#=2(x-3)^2-18+15#
#rArry=2(x-3)^2-3larrcolor(red)"in vertex form"#
#rArrcolor(magenta)"vertex "=(3,-3)#
#color(blue)"Intercepts"#
#• " let x = 0, in equation for y-intercept"#
#• " let y = 0, in equation for x-intercepts"#
#x=0toy=2(-3)^2-3=15larrcolor(red)"y-intercept"#
#y=0to2(x-3)^2-3=0#
#rArr(x-3)^2=3/2#
#color(blue)"take the square root of both sides"#
#rArrx-3=+-sqrt(3/2)larrcolor(blue)"note plus or minus"#
#rArrx=3+-sqrt(3/2)larrcolor(red)"x-intercepts"#
#rArrx~~1.78,x~~4.22" to 2 dec. places"#
