"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 this form use "color(blue)"completing the square"
• " ensure the coefficient of "x^2" term is 1"
• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2+4x
y=x^2+4x+4larr" coefficient of "x^2" term is 1"
y=x^2+2(2)xcolor(red)(+4)color(red)(-4)+1
color(white)(y)=(x+2)^2-3
rArr"vertex "=(-2,-3)
color(blue)"Intercepts"
• " let x = 0, in the equation for y-intercept"
• " let y = 0, in equation for x-intercepts"
x=0toy=4-3=1larrcolor(red)" y-intercept"
y=0to(x+2)^2-3=0
rArr(x+2)^2=3
rArrx+2=+-sqrt3larr" note plus or minus"
rArrx=-2+-sqrt3larrcolor(blue)"exact values"
x~~ -3.73,x~~ -0.27larrcolor(red)" x-intercepts"
