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
Mia
Jun 13, 2016

y=13/25*(x-8)^2-7y=1325⋅(x−8)2−7

Explanation:

The standard form of a parabola is defined as:

y = a*(x-h)^2+ky=a⋅(x−h)2+k

where (h,k)(h,k) is the vertex

Substitute the value of the vertex so we have:

y=a*(x-8)^2 -7y=a⋅(x−8)2−7

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

6= a*(3-8)^2-76=a⋅(3−8)2−7
6 = a*(-5)^2 -76=a⋅(−5)2−7
6 = 25*a -76=25⋅a−7
6+7 = 25*a6+7=25⋅a
13 =25*a13=25⋅a
13/25 = a1325=a

Having the value of a=13/25a=1325 and vertex(8,-7)(8,−7)

The standard form is:

y=13/25*(x-8)^2-7y=1325⋅(x−8)2−7

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