What is the equation of the parabola that has a vertex at # (-4, 121) # and passes through point # (7,0) #?

1 Answer

#y=-(x+4)^2+121#

Explanation:

Given vertex at #(-4, 121)# and a point #(7, 0)#
#h=-4#
#k=121#
#x=7#
#y=0#

Use the standard form. Substitute the values to solve for #p#.

#(x-h)^2=-4p(y-k)#

#(7--4)^2=-4p(0-121)#

#(11)^2=-4p(-121)#
#121=4(121)p#

#121/121=(4(121)p)/121#

#cancel121/cancel121=(4(cancel121)p)/cancel121#

#1=4p#

#p=1/4#

the equation is now

#(x--4)^2=-4(1/4)(y-121)#

#(x+4)^2=-1(y-121)#

#(x+4)^2=-y+121#

#y=-(x+4)^2+121#

graph{y=-(x+4)^2+121[-100,300,-130,130]}

Have a nice day !! from the Philippines.