#"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 constant.
#y=2(x+1)^2+3" is in this form"#
#"with " a=2,h=-1,k=3#
#rArrcolor(magenta)"vertex "=(-1,3)#
#color(blue)"Intercepts"#
#• " let x = 0, in equation for y-intercept"#
#• " let y = 0, in equation for x-intercepts"#
#x=0toy=2(0+1)^2+3=5larrcolor(red)" y-intercept"#
#y=0to2(x+1)^2+3=0#
#rArr(x+1)^2=-3/2#
#"but " (x+1)^2>=0#
#rArr" there are no x-intercepts"#
#color(blue)"Shape of parabola"#
#• " if " a>0" then minimum " uuu#
#• " if " a<0" then maximum " nnn#
#"here " a=2rArr" minimum turning point"#
graph{2(x+1)^2+3 [-10, 10, -5, 5]}
