Graphing+a+Quadratic+Function+in+Standard+Form

Graph a quadratic function in any form and identify the domain and range - Standard form
We are going to graph a quadratic function from Standard Form. For the following function, let's look at the graph and see if we can find the key information that can be found directly from the equation.

**Key Information** As you can see from the graph, the **y-intercept** is (0, 6). If we look at the graph in standard form the **y-intercept** is the "c" value! The **y-intercept is the key information** that we can obtain directly from the equation. So without doing much work we can find the y-intercept. After we find the y-intercept, we will need to find the axis of symmetry, vertex and then graph an additional point. Let's try an example. **Example 1:** Graph the following quadratic function: **y = x 2 - 6x + 4** **1 - Key information** Recall the y-intercept is the c value so the y-intercept is (0, 4). ** 2 - Axis of Symmetry ** In order to find the **axis of symmetry** we will use an equation that is derived from the standard form of a quadratic equation. The axis of symmetry is also the x value of the vertex. math x=\dfrac{\text{-}b}{2a} math In our equation, a = 1 and b = -6. Let's substitute and solve for x. ** 3 - Vertex ** We now have the x - value of the **vertex**, x = 3. In order to find the y - value we will use substitution. Substitute the x - value into the equation and solve for y. So the vertex is (3, -5) ** 4 - Additional Point - Use Symmetry ** To find one more point we will use symmetry. Once we graph the vertex, the line of symmetry and the y-intercept we can use symmetry to find the additional point.

Now watch the video to see how we graph the parabola now that we have the vertex, axis of symmetry and y-intercept. media type="custom" key="27748747"


 * Example 2:** Graph the quadratic equation ** y = -2x 2 +12x - 7 **

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 * Graphing Quadratic Functions Target B Standard Form Quick Check**

Graph the following quadratic function: **y = x 2 - 6x - 4**

Graphing Quadratic Functions Target B Standard Form Quick Check Solutions

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