Learning Objectives:

__Math Tutoring on Solving Quadratic Equations Graphically__

A **quadratic** is a **polynomial** that looks like **ax² + bx + c,** where **a,** **b and c** are just numbers. A **quadratic equation** as you remember is an equation that can be written on the **standard form ax²+bx+c=0,** where **a≠0.** You know by now how to solve a **quadratic equation **using **factoring**. Another way of solving a **quadratic equation** is to solve it **graphically.** The **roots** of a **quadratic equation** are the **x-intercepts** of the graph. The **zeros** of a **quadratic equation** are the points where the** graph **of the** quadratic equation** crosses the **x-axis.** Following are the steps to solve **quadratic equations graphically: **

**Step 1:** Determine which form of **quadratic** **equation** we have, i.e.

**1) Standard form f(x) = ax² + bx + c **where** a, b, and c** are real numbers and **a** is not equal to **zero.**

**2) Vertex form f(x) = a(x - h)² + k **where** a, h, and** **k **are real numbers and **a** does not equal **zero. **

**Step 2:** Define your variables **a, b, **and** c (**or** a, h, **and** k). **

**Step 3:** Calculate **h** and **k.** Plot the **vertex. **

**Step 4:** If necessary, find and plot the **x **and **y intercept. **

**Step 5:** If necessary, **plot** additional points, then **graph.**

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**Hook Questions:**

*1. **How do you graph a function?*

*2. **Are quadratic equations functions?*

*3. **How do you solve an equation graphically?*

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