"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"
