For a function f, the table gives some values of x and their corresponding value of f(x). What is the y-coordinate of the y-intercept of the graph of y=f(x) in the xy-plane?

Question

The table :

1. X=0; f(x)=7
2. X=2; f(x)=8
3. X=5; f(x)=0

Answer 1

(0,7), (2,8), (5,0) are points on a parabola, a quadratic equation with x intercept = 7 and y intercept = 5

It's either a downward opening or rightward opening parabola

for downward opening y = a(x -h)^2 + k where a<0

and (h,k) is the vertex

or y = a(x-c)(x-d) where c and d are x intercepts

y =a(x-5)(x-d)

8 = a(2-5)(2-d) = -5a(3-d)

8 = 5a(d-3)

a = 8/5(d-3) with a<0, -3 1/2 < d<-3 maybe about =-3 1/4

you have 3 points, use them to get 3 equations and 3 unknowns