STEP 1: Recall what is a parabola
https://www.mathsisfun.com/geometry/parabola.html
STEP 2: Recall the standard form of a parabola in vertex form
https://www.qalaxia.com/viewDiscussion?messageId=5d1433777ae99744ef6d360d
The standard form of the equation of any parabola whose vertex is (h, k) is:
f(x)=a(x-h)^{2}+k
The vertex of this parabola is (2, 7)
f(x)=a(x-2)^{2}+7
STEP 3: Find the equation of the parabola that passes through the vertex and the point
This parabola goes through the point (4, 3) so plug in x=4 and f(x)=3
3=a(4-2)^{2}+7
,3=4a+7
-4=4a
-1=a
Therefore the equation of this parabola is:
F(x)=-(x-2)^2+7
