The document discusses three methods for writing quadratic functions from given information: using vertex form when given the vertex and a point, using intercept form when given the x-intercepts and a point, and using a system of equations when given three points. For each method, it provides steps to substitute values into the form, solve for coefficients, and write the function in standard form. It encourages practicing each method.

1. Writing Quadratic
Functions
Algebraic Reasoning

3. Use Vertex form when:
Given the vertex and a point.
1. Substitute values
2. Solve for a
3. Replace vertex and a in vertex form and convert to
standard form

4. Now Practice:

5. Use Intercept form when:
Given the zeros (x-intercepts) and a point.
1. Substitute values
2. Solve for a
3. Replace intercepts and a in intercept form and
convert to standard form

6. Now Practice:

7. Use System of Equations when:
Given the 3 points (graph or table)
1. Substitute values
2. Solve for each variable using systems
3. Replace a, b, and c in standard form

8. Use System of Equations when:
Given the 3 points (graph or table)
1. Substitute values
2. Solve for each variable using systems
3. Replace a, b, and c in standard form

9. Now Practice: