How do you find the vertex and intercepts for #(x − 2)^2 = -12(y − 2)#?
2 Answers
So the curve has:
Vertex: maximum at
Y-intercept:
X-intercepts:
Explanation:
Rearrange for y.
From the completed square form, the maximum turning point is at
For the y-intercept, let
For the x-intercepts, let
So the curve has:
Vertex: maximum at
Y-intercept:
X-intercepts:
graph{(x-2)^2=-12(y-2) [-10, 10, -5, 5]}
Explanation:
#"the quadratic is in standard translated form"#
#•color(white)(x)(x-h)^2=4p(y-k)#
#"is the distance from the vertex to the focus/directrix"#
#rArrcolor(magenta)"vertex "=(2,2)#
#"to find intercepts"#
#• " let x = 0, in the equation for y-intercept"#
#• " let y = 0, in the equation for x-intercepts"#
#x=0to4=-12y+24rArry=5/3larrcolor(red)"y-intercept"#
#y=0to(x-2)^2=24#
#color(blue)"take square root of both sides"#
#x-2=+-sqrt24larrcolor(blue)"note plus or minus"#
#rArrx=2+-2sqrt6larrcolor(red)"x-intercepts"#