Question

Three points on the graph of the function f(x) are {(0,4), (1,9), (2, 16)}. Which

equation represents f(x)?
○ ƒ(x) = 4 · (²)ª
Of(x) = 5x + 4
Of(x) = (x + 2)²
Of(x) = 7x+2
Submit Answer

Answer 1

We can use the three given points to form a system of equations and solve for the coefficients of the polynomial function:

When x = 0, f(x) = 4:

4 = a(0)^2 + b(0) + c

4 = c

When x = 1, f(x) = 9:

9 = a(1)^2 + b(1) + c

9 = a + b + 4

When x = 2, f(x) = 16:

16 = a(2)^2 + b(2) + c

16 = 4a + 2b + 4

We can simplify the second equation by substituting c = 4:

9 = a + b + 4

a + b = 5

Solving for b, we get:

b = 5 - a

Now we can substitute this expression for b in the third equation:

16 = 4a + 2b + 4

16 = 4a + 2(5 - a) + 4

16 = 6a + 14

2 = 6a

a = 1/3

Substituting this value of a in the equation for b:

b = 5 - a

b = 5 - 1/3

b = 14/3

Now we know that the quadratic function that passes through the three points is:

f(x) = (1/3)x^2 + (14/3)x + 4

Therefore, none of the given equations represents f(x). The correct equation is f(x) = (1/3)x^2 + (14/3)x + 4.