This is a quadratic in yy instead of xx
So yy is the independent variable. The consequence is that the graph of type uu∪ is rotated clockwise by 90^o90o
Being given this question suggests that your mathematical manipulation skills are more than basic. So not a lot of explanation is given.
12x=-y^2-6y-3312x=−y2−6y−33
color(red)("Correction:")Correction: as y^2y2 is negative so the graph type of uu∪ would be rotated 90^o90o anticlockwise giving shape sup⊃
x=-1/12y^2-1/2 y-11/4x=−112y2−12y−114
color(blue)("Determine the x-intercept")Determine the x-intercept
Instead of -11/4−114 being the intercept of the y-axis it is the intercept of the x-axis
color(blue)("Determine the y-intercept")Determine the y-intercept
The determinant of form
b^2-4ac""->""(-1/2)^2-4(-1/12)(-11/4) = +1/4-11/12b2−4ac→(−12)2−4(−112)(−114)=+14−1112
=-2/3=−23
As the determinant is negative there is no y-intercept
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color(blue)("Determine vertex")Determine vertex
Write as:" "x=-1/12(y^2 +12/2y)-11/4 x=−112(y2+122y)−114
Consider the 12/2122 from 12/2y122y
=>y_("vertex")=(-1/2)xx12/2 = -3⇒yvertex=(−12)×122=−3
Substituting y=-3y=−3
x_("vertex")=-1/12(-3)^2-1/2(-3)-11/4 xvertex=−112(−3)2−12(−3)−114
x_("vertex")= -3/4 +3/2-11/4 = -2 xvertex=−34+32−114=−2
"Vertex" -> (x,y)=(-2,-3)Vertex→(x,y)=(−2,−3)
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