"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"
"to obtain y in this form use "color(blue)"completing the square"
• " the coefficient of the "x^2" term must be 1"
rArry=3(x^2+5/3x+3)
• " add/subtract "(1/2"coefficient of x-term")^2" to"
x^2+5/3x
y=3(x^2+2(5/6)xcolor(red)(+25/36)color(red)(-25/36)+3)
color(white)(y)=3(x+5/6)^2-25/12+9
color(white)(y)=3(x+5/6)^2+83/12larrcolor(red)"in vertex form"
rArrcolor(magenta)"vertex "=(-5/6,83/12)
color(blue)"Intercepts"
• " let x = 0, in the equation for y-intercept"
• " let y = 0, in the equation for x-intercepts"
x=0toy=3(5/6)^2+83/12=9larrcolor(red)"y-intercept"
y=0to3(x+5/6)^2+83/12=0
rArr3(x+5/6)^2=-83/12
rArr(x+5/6)^2=-83/36
"this has no real solutions hence no x-intercepts"
graph{3x^2+5x+9 [-20, 20, -10, 10]}
