What is the equation of the parabola that has a vertex at # (2, -9) # and passes through point # (12, -4) #?

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Answer 1 · 2018-06-10T10:11:13

#y=1/20(x-2)^2-9# in Vertex Form of the equation

Given:
Vertex#->(x,y)=(2-9)#
Point on curve #->(x,y)=(12,-4)#

Using the completed square format of a quadratic

#y=a(x+b/(2a))^2+k#

#y=a(xcolor(red)(-2))^2color(blue)(-9)#

#x_("vertex")=(-1)xx(color(red)(-2)) = +2" "# Given value
#y_("vertex")=color(blue)(-9)" "# Given value

Substituting for the given point

#-4=a(12-2)^2-9#

#-4=a(100)-9#

#a=5/100=1/20# giving:

#y=1/20(x-2)^2-9# in Vertex Form of the equation

Tony B