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