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)

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