Learning Objectives:

__Math Tutoring on ____Determining Equations of Quadratic Functions__

When we are not given the equation of a **Quadratic Function**, in order to obtain the equation of a **Quadratic** **Function**, some information must be given. If we are given the **vertex**, in **Vertex Form** we can find an equation of a **Quadratic Function** as follows:

1. Plug in the vertex.

2. Simplify, if necessary.

3. Plug in **x & y** coordinates of the point given.

4. Solve for **"a".**

5. Now substitute **"a"** and the vertex into the vertex form.

In math tutoring when we are given three points of a **Quadratic Function**, in **General Form** we can find the equation that defines the **function** in the following way:

1. Plug in the coordinates for **x** and **y** into the general form. Remember **y** and **f(x)** represent the same quantity.

2. Simplify. (Remember the order of operations)

3. Repeat steps 1 & 2 for the other two points.

4. Take two equations at a time and eliminate one variable (**c** works well)

5. Then repeat using two equations and eliminate the same variable you eliminated in #4.

6. Take the two resulting equations and solve the system (you may use any method).

7. After finding two of the variables, select an equation to substitute the values back into.

8. Find the third variable.

9. Substitute **a, b, and c** back into the general equation.

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**Hook questions:**

*1. **How do you know if it is a quadratic function?*

*2. **How do you find the equation of a function?*

*3. **How do you find the vertex of a quadratic function in standard form?*

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