What is the equation of the parabola that has a vertex at # (-18, 2) # and passes through point # (-3,-7) #?

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Answer 1 · 2017-04-26T10:23:34

In vertex form we have:

#y=-1/25(x+18)^2+2#

We can use the vertex standardised form:

#y=a(x+d)^2+k#

As the vertex #->(x,y)=(color(green)(-18),color(red)(2))#

Then #(-1)xxd=color(green)(-18)" "=>" "d=+18#

Also #k=color(red)(2)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So now we have:

#y=a(x+d)^2+k" "->" "y=a(x+18)^2+2#

Using the given point of #(-3,-7)# we substitute to determine #a#

#y=a(x+18)^2+2" "->" "-7=a(-3+18)^2+2#

#" "-7=225a+2#

#" "(-7-2)/225=a#

#" "a=-1/25#

Thus #y=a(x+d)^2+k" "->" "y=-1/25(x+18)^2+2#

Tony B