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# A First look at Parabola Graphing

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## Instructions

1. Click and drag on the different colored "handles" to change the coefficients of the quadratic equation
2. If something goes away, it is probably because you made something zero!

## Questions

1. Where is the vertex of x2+4x-5?

2. Where are the roots (zeros) of x2+4x-5?

3. The green version of the function on the second line is what you would have if you used the "Complete the Square" method to get the function in the a(x-h)2 + k form. Do you think this form is better for finding the roots or the vertex?

4. In Algebra I you learned that if ax2+bx+c=0, then x=(-b±sqrt(b2-4ac)÷2a. The top form of the formula f(x)=ax2+bx+c looks like a quadratic equation. Do you think this form is better for finding the roots or the vertex?

5. What values of a, b, and c make a parabola whose vertex is at (3,0)?

6. What values of a, b, and c make a parabola whose vertex is at (3,0), but going in the opposite direction as the equation you found in question 1?

7. What seems to make the parabola go concave up or concave down: a, b or c?

8. What seems to make the parabola more narrow or wide: a, b, or c?

9. What seems to make the parabola's vertex go up and down: a, b, or c?

10. What seems to control the location of the axis of symmetry: a, b, or c?

11. Find a function that has the vertex at (0, -8) and roots at -4 and 4

12. Find a function that has the vertex at (0, +8) and roots at -4 and 4

13. What are the roots of (-2/5)x2-4x+(9/2)?

14. What are the roots of 2x2+8x-1?

15. Some functions have roots that are real numbers, others only have roots that are complex numbers. By looking at the graph alone, how can you tell the difference?

Here is Fr. Chris' source code: parabola.java