#"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 "color(blue)"completing the square"#
#• " ensure coefficient of "x^2" term is 1"#
#• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2+6x#
#rArry=x^2+2(3)xcolor(red)(+9)color(red)(-9)-16#
#color(white)(rArry)=(x+3)^3-25#
#rArrcolor(magenta)"vertex "=(-3,-25)#
#color(blue)"Intercepts"#
#• " let x = 0, in the equation for y-intercept"#
#• " let y = 0, in the equation for x-intercepts"#
#x=0toy=-16larrcolor(red)" y-intercept"#
#y=0to(x+3)^2-25=0#
#rArr(x+3)^2=25#
#color(blue)"take the square root of both sides"#
#rArrx+3=+-5larr" note plus or minus"#
#rArrx=+-5-3#
#rArrx=2" or "x=-8larrcolor(red)" x-intercepts"#
