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Using the direction, size and vertex of your parabola, think of a quadratic equation in general form, y = a(x - h)2 + k, that would closely match your parabola. Remember (h, k) represents the vertex of the parabola. Enter that equation in the Input bar.
See how closely the graphed parabola matches your image parabola. You may need to try different values of a to make the parabola fit. To change the values of the equation, right-click on the parabola, choose Object Properties…, and change the equation under the Basic tab. Close the window.
Once the graphed parabola matches as close as possible to the image, make note of the quadratic equation, both in general and standard form (y = ax2 + bx + c). When completed, the graphed parabola should lie on top of the parabola in your image. If necessary, right-click on the image and go to the Color tab to make the image more transparent so the graphed parabola can be seen over the image.
Identify the vertex, axis of symmetry, domain and range of the graphed parabola by inspecting your graph.
Find the x- and y-intercepts of the parabola using the "Intersect Two Objects" icon . Remember this tool may be hidden below other buttons. To find the x-intercepts, select the parabola, then the x-axis. To find the y-intercepts, select the parabola, then the y-axis.
Find the discriminant and explain the best method of finding the x-intercepts algebraically.
Find the x-intercepts, or solutions to the quadratic equation, algebraically using each of the following methods: factoring, the quadratic formula, and completing the square. If a method cannot be used, explain why. Show all work involved with each method.
Write a paragraph or two describing the picture you took. Provide details such as where it was found, how you found it, and why you chose this parabola in your activity.