Final answer:
The graph represented by the given points passes through the vertex of a parabola. To find the equation of this parabola...
Step-by-step explanation:
The graph represented by the given points passes through the vertex of a parabola. To find the equation of this parabola, we can use the standard form of a parabola equation, which is y = ax² + bx + c. We have three points, (0,5), (1,4), and (2,5), which satisfy this equation. Plugging in the values for each point, we can solve for the coefficients a, b, and c. First, let's take the point (0,5).
Substituting x = 0 and y = 5 into the equation, we get:
5 = a(0)² + b(0) + c
5 = c
Now, let's take the point (1,4).
Substituting x = 1 and y = 4 into the equation, we get:
4 = a(1)² + b(1) + 5
4 = a + b + 5
-1 = a + b
Finally, let's take the point (2,5).
Substituting x = 2 and y = 5 into the equation, we get:
5 = a(2)² + b(2) + 5
5 = 4a + 2b + 5
0 = 4a + 2b
Solving the system of equations formed by these three equations, we can find the values of a and b. Once we have the values of a, b, and c, we can write the equation of the parabola.