An equation of the graph shown could be:

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The problem asks us to identify which equation could represent the graph shown. We note the graph has a parabola opening upward and appears to have its vertex at (-1, 2), with a point at (0, 5) labeled on the curve.

Option 1: y = (x - 1)^2 + 4. This is a parabola with vertex at (1, 4). Since the vertex is at (1, 4), this does not match the observed vertex (-1, 2). Therefore, this option is inconsistent with the graph’s location of the axis and vertex.

Option 2: y = (x - 1)^2 + 2. This has vertex at (1, 2). Again, the vertex is at x = 1, not x = -1, so the graph would be shifted to the right. This does not align with the (-1, 2) vertex observed.

Option 3: y = 2(x + 1)^2 + 2. This is of the form y = a(x - h)^2 + k with h = -1 and k = 2, giving a vertex at (-1, 2). The graph’s vertex matches this location well. However, to verify fully, we should check another known point: at x = 0, y = 2(1)^2 + 2 = 4. If the graph shows (0, 5) on the curve, this option would place the point (0, 4) on the curve, which disagrees with (0, 5). So while the vertex aligns, this option may fail to match the given additional point.

Option 4: y = x^2 + 5. This is a standard upward parabola with vertex at (0, 5). The vertex here is at x = 0, not at x = -1, so it does not correspond to the shifted vertex suggested by the graph. This option does not fit the observed vertex.

Option 5: y = 3(x + 1)^2 + 2. This has the vertex at (-1, 2) as well, because it is of the form y = a(x - h)^2 + k with h = -1 and k = 2. The coefficient a = 3 makes the parabola steeper than option 3. Checking the point x = 0, we get y = 3(1)^2 + 2 = 5, which matches the labeled point (0, 5) on the graph. This option is consistent with both the vertex and the additional point provided.

In summary, each option’s alignment with the vertex and the given point is essential. Options 1 and 2 place the vertex at (1, 4) and (1, 2) respectively, which contradict the observed vertex at (-1, 2). Option 4 places the vertex at (0, 5), also inconsistent with the graph. Option 3 places the vertex at (-1, 2) but would yield (0, 4), not (0, 5). Option 5 places the vertex at (-1, 2) and, with x = 0, gives y = 5, exactly matching the labeled point on the graph. These considerations guide how each choice aligns or misaligns with the graph’s geometry.

MATH 1151 AU2025 (18443) Calculus Concept Readiness Assessment (CCR)

An equation of the graph shown could be:

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