Part 1Sketch the graph of the parabola by using the vertex, the y-intercept, and the x-intercepts. Check the graph using a calculator.yequals=negative 3−3xsquared2plus+66xplus 4+4 Part 1The vertex is [input]enter your response here .(Type an ordered pair.) Part 1
-12-10-8-6-4-224681012-12-10-8-6-4-224681012xy Edit coordinates (0,0) interactive graph

Question

Part 1Sketch the graph of the parabola by using the​ vertex, the​ y-intercept, and the​ x-intercepts. Check the graph using a calculator.yequals=negative 3−3xsquared2plus+66xplus 4+4 Part 1The vertex is [input]enter your response here .​(Type an ordered​ pair.) Part 1
-12-10-8-6-4-224681012-12-10-8-6-4-224681012xy Edit coordinates (0,0) interactive graph

BlackTom AI · Accepted Answer

We begin by identifying what the question is asking. The prompt states: The vertex is [input] (Type an ordered pair.). This is asking us to provide the coordinates of the parabola's vertex.

First, I will consider the given quadratic expression as best as can be interpreted from the garbled text. It appears to resemble a standard form such as y = a x^2 + b x + c, with possible coefficients that might be -3, 66, and 4 or something similar. However, the exact coefficients are unclear due to the formatting issues in the prompt. This matters because the vertex location depends on these coefficients.

Option/observation 1: If we had a quadratic in the form y = a x^2 + b x + c, the x-coordinate of the vertex is given by x_v = -b/(2a). The y-coordinate would then be y_v = a x_v^2 + b x_v + c.

Observation 2: The provided answer for the vertex is (2, 10). If we plug x = 2 into a generic vertex formula, we would obtain y_v = a(2)^2 + b(2) + c. For this to equal 10, the constants a, b, c must satisfy 4a + 2b + c = 10.

Now, let me test consistency with possible typical forms:
- If the quadratic were y = -3x^2 + 66x + 4 (a = -3, b = 66, c = 4), then x_v = -b/(2a) = -66/(-6) = 11, and y_v would be 367. The vertex (11, 367) is far from (2, 10), so this cannot be the correct interpretation.
- If instead the vertex is (2, 10), that implies x_v = 2. Using x_v = -b/(2a), we require -b/(2a) = 2, i.e., b = -4a. Then y_v = c - b^2/(4a) or, more directly, y_v = a(2)^2 + b(2) + c. Substituting b = -4a gives y_v = 4a + (-8a) + c = -4a + c. Setting this equal to 10 yields c = 10 + 4a. Without exact a, b, c, we cannot confirm whether the given coefficients match this.

Observation 3: Given the ambiguity in the coefficient string, the stated vertex (2, 10) could be correct for a quadratic with appropriate coefficients, but it does not align with the clearly readable portion that resembles -3x^2 + 66x + 4. This discrepancy suggests a transcription or parsing error in the problem statement, rather than a fundamental math mistake.

To reconcile: if your assignment intentionally asks for the vertex and the provided correct answer is (2, 10), then the underlying quadratic must have x-coordinate of the vertex equal to 2, and the resulting y-value at x = 2 must be 10. This would correspond to a relationship 4a + 2b + c = 10 with b = -4a. If you can retrieve the exact coefficients from the source (or re-check the transcript), you can confirm the vertex precisely.

In absence of a clearly stated, consistent quadratic, we cannot independently derive (2, 10) as the vertex from the garbled expression. The key points to avoid common pitfalls are: (1) remember x_v = -b/(2a) for ax^2 + bx + c, (2) compute y_v by substituting x_v back into the equation, and (3) verify that the given vertex aligns with the actual coefficients.

If you provide the exact intended equation (the precise a, b, and c), I can recompute the vertex step by step and confirm whether (2, 10) is correct or identify the correct vertex for that equation.

Homework:Module 7 Homework (Quadratics)

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.

An equation of the graph shown could be:

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