Write the Equation Parabola has a vertex at (2,5) and passes through the point (3,7)

Question

asked Mar 19, 2019 36.2k views

1 Answer

Athif Saheer · Answer 1 · 2019-03-26T03:31:21+0000

Given a vetex (h,k) of a function parabola, the corresponding equation is:

f(x)=a(x-h)^2+k

With (h,k)=(2,5) we get the equation:

f(x)=a(x-2)^2+5

In order to find a, we use the given point (3,7) like this:

$7=a(3-2)^2+5\\7=a+5\\a=7-5=2$
The equation is then:

f(x)=2(x-2)^2+5