Question

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

Answer 1

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`