The values : f(-2) = 2
f(0) = 1/2
f(4) = 8 .
The function given by the graph appears to be a quadratic function, which means it's of the form f(x) = ax^2 + bx + c.
We can use the graph to determine the values of a, b and c, and then use the equation to find the specific function values you're interested in.
The graph intersects the x-axis at two points, which means there are two roots to the quadratic equation.
The roots are approximately -2 and 4. We can use these roots to solve for a and b in the quadratic equation:
f(x) = a(x - (-2))(x - 4)
f(x) = a(x + 2)(x - 4)
Expanding this equation gives:
f(x) = ax^2 + (-4a - 2b)x + (8a - 8b)
We can also see from the graph that the function passes through the point (0, 2).
This means that f(0) = 2. We can plug this into our equation to solve for c:
2 = a(0)^2 + (-4a - 2b)(0) + (8a - 8b)
2 = 8a - 8b
a - b = 1/4
Now we have two independent equations to solve for a and b:
a - b = 1/4
-2a + 4b = 0 (obtained by setting x = 2 in the quadratic equation)
Solving for a and b, we get:
a = 1/2
b = -1/4
Therefore, the function is:
f(x) = (1/2)x^2 + (-1/4)x + (1/2)
Now we can find the specific function values you're interested in:
f(-2) = (1/2)(-2)^2 + (-1/4)(-2) + (1/2) = 2
f(0) = (1/2)(0)^2 + (-1/4)(0) + (1/2) = 1/2
f(4) = (1/2)(4)^2 + (-1/4)(4) + (1/2) = 8
So, the values you requested are:
f(-2) = 2
f(0) = 1/2
f(4) = 8.