Question

which is the minimum or maximum value of the given function?
graph of a parabola opening upwards, with vertex around (-2, -4) and passing through (0, 0) etc.
a. the function has a minimum value of -3.
b. the function has a minimum value of -4.
c. the function has a maximum value of -3.
d. the function has a maximum value of -4.

Explanation:

Step1: Analyze the parabola's direction

The parabola opens upwards (since it curves upward), so it has a minimum value (the vertex is the lowest point).

Step2: Identify the vertex's y - coordinate

Looking at the graph, the vertex (the lowest point of the parabola) has a y - coordinate of - 4? Wait, no, wait. Wait, let's check the grid. Wait, the vertex seems to be at y=-4? Wait, no, maybe I misread. Wait, the options: let's re - examine. Wait, the graph: the lowest point (vertex) is at y = - 4? Wait, no, option B says minimum value of - 4, option A says - 3. Wait, looking at the grid, the vertex is at ( - 2, - 4)? Wait, no, the y - axis: the grid lines. Let's see, the parabola's lowest point (vertex) has a y - value of - 4? Wait, no, maybe I made a mistake. Wait, the options: A is minimum - 3, B is minimum - 4, C is maximum - 3, D is maximum - 4. Since the parabola opens upwards, it has a minimum. Now, looking at the graph, the vertex (the bottom of the parabola) is at y=-4? Wait, no, let's check the y - axis. The y - axis has marks at 5,4,3,2,1,0, - 1, - 2, - 3, - 4, - 5. The lowest point of the parabola is at y=-4? Wait, no, maybe the vertex is at y = - 4? Wait, the option B says "The function has a minimum value of - 4". Wait, but let's check again. Wait, maybe I misread the graph. Wait, the parabola: when x is - 2, what's the y - value? Let's see the grid. Each square is 1 unit. The vertex is at ( - 2, - 4)? Wait, no, maybe the y - value is - 4? Wait, the options: B is minimum - 4. Wait, but let's confirm. The parabola opens upwards, so it has a minimum. The minimum value is the y - coordinate of the vertex. From the graph, the vertex (the lowest point) has a y - coordinate of - 4? Wait, no, maybe I made a mistake. Wait, the option B is "The function has a minimum value of - 4". Wait, but let's check the options again. Wait, maybe the vertex is at y=-4. So the correct option is B.

Wait, no, wait, maybe I misread. Let me check again. The graph: the parabola's lowest point (vertex) is at y = - 4? Wait, the y - axis: the numbers are 5,4,3,2,1,0, - 1, - 2, - 3, - 4, - 5. The vertex is at ( - 2, - 4)? So the minimum value is - 4. So option B.

Answer:

B. The function has a minimum value of -4.