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2) Sk 1) Graph the equation y = 2x? - 2x - 12 Axis of Symmetry: Vertex: ( y-intercept: ( x-intercept(s): Axis of Symmetry: Vertex: (, ) y-intercept: ( x-intercept(s): (. )

2) Sk 1) Graph the equation y = 2x? - 2x - 12 Axis of Symmetry: Vertex: ( y-intercept: ( x-intercept(s): Axis of Symmetry: Vertex: (, ) y-intercept: ( x-intercept(s): (. )

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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This educational exercise involves graphing quadratic equations and identifying key features such as the axis of symmetry, vertex, y-intercept, and x-intercepts. **Problem 1:** Graph the equation: \(y = 2x^2 - 2x - 12\) **Steps and Explanation:** 1. **Equation Given:** - \(y = 2x^2 - 2x - 12\) 2. **Features to Identify:** - **Axis of Symmetry:** This is a vertical line that passes through the vertex of the parabola. It can be found using the formula \(x = -\frac{b}{2a}\). - **Vertex:** This is the highest or lowest point on the graph of the parabola. Use the x-value from the axis of symmetry and the equation to find the y-value. - **Y-Intercept:** The point where the graph crosses the y-axis, found by setting \(x = 0\). - **X-Intercepts:** Points where the graph crosses the x-axis, found by setting \(y = 0\) and solving for \(x\). 3. **Graph:** - On the grid provided, plot the points that correspond to the above features and sketch the parabola. 4. **Key Points to Record:** - Axis of Symmetry: (\_\_\_\_) - Vertex: (\_\_\_, \_\_\_) - Y-Intercept: (\_\_\_, \_\_\_) - X-Intercepts: (\_\_\_, \_\_\_), (\_\_\_, \_\_\_) **Problem 2:** Sketch the equation: \(y = -(x + 4)^2 - 3\) **Steps and Explanation:** 1. **Equation Given:** - \(y = -(x + 4)^2 - 3\) 2. **Features to Identify:** - **Axis of Symmetry:** This is a vertical line that passes through the vertex of the parabola. For this equation, it’s at \(x = -4\) because the equation is in the form \(y = a(x - h)^2 + k\). - **Vertex:** This can be found directly from the equation. The vertex is \((-4, -3)\). - **Y-Intercept:** The point where the graph crosses the y-axis
Transcribed Image Text:This educational exercise involves graphing quadratic equations and identifying key features such as the axis of symmetry, vertex, y-intercept, and x-intercepts. **Problem 1:** Graph the equation: \(y = 2x^2 - 2x - 12\) **Steps and Explanation:** 1. **Equation Given:** - \(y = 2x^2 - 2x - 12\) 2. **Features to Identify:** - **Axis of Symmetry:** This is a vertical line that passes through the vertex of the parabola. It can be found using the formula \(x = -\frac{b}{2a}\). - **Vertex:** This is the highest or lowest point on the graph of the parabola. Use the x-value from the axis of symmetry and the equation to find the y-value. - **Y-Intercept:** The point where the graph crosses the y-axis, found by setting \(x = 0\). - **X-Intercepts:** Points where the graph crosses the x-axis, found by setting \(y = 0\) and solving for \(x\). 3. **Graph:** - On the grid provided, plot the points that correspond to the above features and sketch the parabola. 4. **Key Points to Record:** - Axis of Symmetry: (\_\_\_\_) - Vertex: (\_\_\_, \_\_\_) - Y-Intercept: (\_\_\_, \_\_\_) - X-Intercepts: (\_\_\_, \_\_\_), (\_\_\_, \_\_\_) **Problem 2:** Sketch the equation: \(y = -(x + 4)^2 - 3\) **Steps and Explanation:** 1. **Equation Given:** - \(y = -(x + 4)^2 - 3\) 2. **Features to Identify:** - **Axis of Symmetry:** This is a vertical line that passes through the vertex of the parabola. For this equation, it’s at \(x = -4\) because the equation is in the form \(y = a(x - h)^2 + k\). - **Vertex:** This can be found directly from the equation. The vertex is \((-4, -3)\). - **Y-Intercept:** The point where the graph crosses the y-axis
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