How do you write the standard form of the equation of the parabola that has a vertex at (8,-7) and passes through the point (3,6)?

1 Answer
Jun 13, 2016

Answer:

#y=13/25*(x-8)^2-7#

Explanation:

The standard form of a parabola is defined as:

# y = a*(x-h)^2+k#

where #(h,k)# is the vertex

Substitute the value of the vertex so we have:

# y=a*(x-8)^2 -7#

Given that the parabola passes through point #(3,6)# ,so the coordinates of this point verifies the equation, let's substitute these coordinates by #x=3# and #y=6#

# 6= a*(3-8)^2-7#
#6 = a*(-5)^2 -7#
#6 = 25*a -7#
#6+7 = 25*a#
#13 =25*a#
#13/25 = a#

Having the value of #a=13/25# and vertex#(8,-7)#

The standard form is:

#y=13/25*(x-8)^2-7#