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Write an equation (any form) for the quadratic graphed below 4 -5 4 3 -2 -1 2 3 4 -2 -3 -4- y =

Write an equation (any form) for the quadratic graphed below 4 -5 4 3 -2 -1 2 3 4 -2 -3 -4- y =

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The points I picked are (3,4) and (3,2) I can figure out how to get it in

y=a(x-h)²+2

**Quadratic Equation Challenge: Graph Interpretation** In this exercise, you are given a quadratic graph, and your task is to determine the equation of the quadratic function depicted. ### Instructions: - Observe the given graph carefully. - Identify key characteristics such as the vertex, the direction of the parabola (whether it opens upwards or downwards), and the x-intercepts if visible. - Use these observations to derive the equation of the quadratic function. You can write the equation in any of the standard forms (vertex form, standard form, or factored form). ### Graph Details: - The graph depicts a parabola that opens downwards. - The vertex of the parabola is at the point (2, 4). - The parabola intersects the y-axis at y = -4 and appears to cross the x-axis at approximately x = 1 and x = 3. ### Formulas to Recall: - **Standard Form**: \( y = ax^2 + bx + c \) - **Vertex Form**: \( y = a(x-h)^2 + k \) - **Factored Form**: \( y = a(x - r1)(x - r2) \) ### Determine the Equation: Using the vertex form of a quadratic equation, \( y = a(x-h)^2 + k \), where (h, k) is the vertex, we identify (2, 4) as the vertex. The negative vertical orientation suggests 'a' is negative. **Given:** - \( h = 2 \) - \( k = 4 \) - Vertex: (2, 4) ### Your Task: Fill in the blank with the correct equation based on your observation and understanding from the diagram: \[ y = \] This exercise aims to reinforce your understanding of quadratic equations and graph interpretations, helping build strong foundations in algebra.
Transcribed Image Text:**Quadratic Equation Challenge: Graph Interpretation** In this exercise, you are given a quadratic graph, and your task is to determine the equation of the quadratic function depicted. ### Instructions: - Observe the given graph carefully. - Identify key characteristics such as the vertex, the direction of the parabola (whether it opens upwards or downwards), and the x-intercepts if visible. - Use these observations to derive the equation of the quadratic function. You can write the equation in any of the standard forms (vertex form, standard form, or factored form). ### Graph Details: - The graph depicts a parabola that opens downwards. - The vertex of the parabola is at the point (2, 4). - The parabola intersects the y-axis at y = -4 and appears to cross the x-axis at approximately x = 1 and x = 3. ### Formulas to Recall: - **Standard Form**: \( y = ax^2 + bx + c \) - **Vertex Form**: \( y = a(x-h)^2 + k \) - **Factored Form**: \( y = a(x - r1)(x - r2) \) ### Determine the Equation: Using the vertex form of a quadratic equation, \( y = a(x-h)^2 + k \), where (h, k) is the vertex, we identify (2, 4) as the vertex. The negative vertical orientation suggests 'a' is negative. **Given:** - \( h = 2 \) - \( k = 4 \) - Vertex: (2, 4) ### Your Task: Fill in the blank with the correct equation based on your observation and understanding from the diagram: \[ y = \] This exercise aims to reinforce your understanding of quadratic equations and graph interpretations, helping build strong foundations in algebra.
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