An equation of the graph shown could be:

Question

BlackTom AI · Accepted Answer

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:

查看解析

登录即可查看完整答案

类似问题

Quadratic Function For the function defined by , find the following values. Simply your answers. [Fill in the blank] [Fill in the blank] [Fill in the blank] [Fill in the blank]

Let be a quadratic function. Suppose we have given the following information: and . Which of the following answers are correct (Please note that exactly two are correct). If you cannot find the formula of the function, you still can find the shape of its graph by using a graphical argument.

The graph of [math: y] versus [math: x2] x^2 is shown. The rule connecting [math: y] and [math: x] is :

MTH1010_05_10_4

MTH1010_05_04_1

Apply your understanding of quadratic functions and transformations, and sketch: 𝑦 = 0.25 ( 𝑥 + 6 ) 2 − 4 In this quiz, type the y-intercept in the box. AND Sketch on paper. Label the vertex and the intercepts, with their coordinates. (Answer in quiz: 1 mark) (Written answer: 2 marks)

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单