Quadratic Equations using a TI 83 Plus Graphing Calculator

This paragraph introduces the concept of graphing quadratic equations using a TI-83 Plus graphing calculator. It explains that the graph of a quadratic equation is a parabola, an U-shaped curve. The key aspects of a parabola that are discussed include finding the vertex, axis of symmetry, roots, and Y-intercept. The paragraph begins with a simple equation, y = x^2 - 6x + 5, and breaks down the parts of a quadratic equation: the quadratic part (x^2), the linear part (-6x), and the constant part (5). It emphasizes the importance of understanding these components to accurately graph the equation.

The paragraph demonstrates how to enter the quadratic equation into the graphing calculator and use the zoom 6 option to visualize the parabola. It explains that the vertex of the parabola can be found using the calculator's minimum feature. The process involves setting bounds and allowing the calculator to guess the minimum point, which in this case is (-3, -4). The paragraph then describes how to verify the vertex by calculating the Y value when x is -3, confirming that the vertex is indeed at (-3, -4). It also briefly touches on sketching the graph on paper based on the calculated points.

This paragraph focuses on finding the axis of symmetry and the roots of the parabola. The axis of symmetry is determined as the line where x equals the x-value of the vertex, which is x = 3 in this case. The roots, or the points where the parabola intersects the x-axis, are found using the calculator's zero feature. The process involves setting bounds and using the calculator to guess the roots, which are found to be x = 1 and x = 5. The paragraph emphasizes the importance of careful selection of bounds to avoid errors and ensure accurate results.

The paragraph discusses the use of the zoom fit option to adjust the viewing window when dealing with parabolas that do not fit well within the default window settings. It explains that the zoom fit option can rescale the graph to display the entire parabola on the screen. The paragraph then describes how to fine-tune the window by adjusting the minimum and maximum values for the x and y axes to get a clearer view of the parabola's key points, such as the roots and vertex.

The paragraph presents a more complex parabola equation, 4x^2 - 7x - 19, and guides through the process of finding its vertex, axis of symmetry, roots, and Y-intercept. It explains the steps of using the calculator's minimum feature to find the vertex coordinates, which are approximately (8.88, -22.06). The axis of symmetry is calculated as x = 8.88, and the roots are found to be x = 1.47 and x = 3.22 using the zero feature. The Y-intercept is determined as -19 by calculating the value when x is zero. The paragraph concludes with a brief overview of sketching the parabola on paper based on the calculated points.