What is the equation of the parabola that has a vertex at # (-12, 11) # and passes through point # (-9,-16) #?

Answer 1

Eli Assouline

#(x+12)^2=1/3(y-11)#

#"the equation of a parabola "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"#

#"here "(h,k)=(-12,11)#

#rArry=a(x+12)^2+11#

#"to find a substitute "(-9,-16)" into the equation"#

#-16=9a+11rArra=3#

#rArry=3(x+12)^2+11#

#rArr(x+12)^2=1/3(y-11)larrcolor(blue)"is the equation"#

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Answer 2

Julia Adams

The equation of the parabola is (y = -\frac{1}{9}(x + 12)^2 + 11).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.