Writing the equation of a quadratic function given its graph

Question

Find the equation of the quadratic function F whose graph is shown below.

(6,10)

(4,2)

F(x) =

Answer 1

4 standard possibilities, up or downward, right or leftward opening paraboloas.

try the upward opening with vertex at the lower point (2,4)

and through (6,10) y=a(x-2)^2 +4

plug in x=6, y=10 to solve for a

10=a(6-2)^2 + 4

10=16a +4

16a = 6

a =6/16 = 3/8 =0.375

y=F(x) = (3/8)(x-2)^2 + 4 is the most standard quadratic equation through the two points, using one as the vertex

use the same method to get 3 other standard parabolas

but there's an infinite number of quadratics through the two points

you don't seem to have a graph "shown below," as that might narrow down what you're looking for.