Discover how changing coefficients changes the shape of a curve. View the graphs of individual terms (e.g. y=bx) to see how they add to generate the polynomial curve. Generate definitions for vertex, roots, and axis of symmetry. Compare different forms of a quadratic function. Define a curve by its focus and directrix.
Sample Learning Goals:
- Describe how changing the coefficients of a quadratic function changes the graph of the function.
- Predict how the graph of a parabola will change if the coefficients or constant are varied.
- Identify the vertex, axis of symmetry, roots, and directrix for the graph of a quadratic equation.
- Use the vertex form of a quadratic function to describe the graph of the function.
- Describe the relationship between the focus and directrix and resulting parabola.
- Predict the graph of a parabola given a focus and directrix.
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