Graphing+a+Quadratic+Function+in+Vertex+Form

Graphing a Quadratic Function Target B in Vertex Form
We are going to graph a quadratic function from Vertex 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.

As you can see from the graph, the vertex is (3, 2). If we look at the equation in vertex form we can see the vertex (I think the name gave it away)!! As you learned previously in Target A the vertex (h, k) can be found very easily when the quadratic equation is in vertex form. The **vertex is the key information** that we can obtain directly from the equation. If you need to review finding the vertex when a quadratic equation is in vertex form click the following link: Graphing Quadratic Functions - Target A - Quadratic Comparison.
 * Key Information **

Example 1: Graph the function: y = (x - 2) 2 + 3

From the equation, we see the vertex: (2, 3). This also tells us that our axis of symmetry is x = 2. This is the first of our three points we need to graph the parabola.
 * 1 - Key Information**

To find another point we will substitute in a number in for x in the equation and solve for y. You can choose any x value you would like since the domain of the function is all real numbers. But when you are choosing your x value pick an x value that is to the left or right of the x value of the vertex. Let's choose an x value to the left of the x value of the vertex, x = 0. Substituting this value into the function. The additional point is (0, 7) - which happens to be the y-intercept.
 * 2 - Additional Point**

In order to find the third point we will use the symmetry of the parabola to find it. Let's graph the vertex, the axis of symmetry and the additional point first. Once you have graphed the additional point, then use symmetry about the axis of symmetry to find the third point. See below.
 * 3 - Use Symmetry to Find a Third Point: **

Lastly, we need the domain and range. As we stated previously the domain is all real numbers. As for the range, remember it is is determined by the vertex. Our vertex is a minimum with a y-value of 3 so the range is y is greater than or equal to 3.

math \text{Domain: All Real Numbers} \\ \text{Range:} \ y \geq 3 math

Example 2: Graph the following function: **f(x) = - (x - 2)** ** 2 + 1 **

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 * Graphing a Quadratic Function Target B in Vertex Form Quick Check **

Graph the following quadratic function in vertex form **f(x) = (x + 4)** ** 2 ** **- 5**.

Graphing a Quadratic Function Target B in Vertex Form Quick Check Solutions

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