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# ZingPath: Graphs and Polynomials

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## Graphs and Polynomials

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### Lesson Focus

#### Graphing a Quadratic Function: Vertex Form

Algebra-2

You will graph a quadratic function given in vertex form by determining the vertex, axis of symmetry, orientation, and intercepts.

### Now You Know

After completing this tutorial, you will be able to complete the following:

• Find the vertex of a quadratic function given in vertex form.
• Find the axis of symmetry of a quadratic function given in vertex form.
• Find the orientation of a quadratic function given in vertex form.
• Find the y–intercept of a quadratic function given in vertex form.
• Find the x–intercepts of a quadratic function given in vertex form.
• Graph a quadratic function given in vertex form.

### Everything You'll Have Covered

The x- and y-intercepts are often useful when graphing quadratic functions.

In addition to the vertex and axis of symmetry, the points where the parabola crosses the x- and y-axis are often used when graphing quadratic functions; these points are referred to as the x- and y-intercepts, respectively.

The easiest method of calculating the y-intercept, using the vertex form of the quadratic function, is to evaluate f(0). Using the above example, f(0) = 2(0 + 2)^2 - 3 = 5, the y-intercept of the quadratic function f(x) = 2(x + 2)^2 - 3 is the point on the y-axis (0, 5). It should be noted, that for a relationship to be a function, the function can have only one y-intercept.

While, calculating the y-intercept is straight forward, the same cannot be said of about the x-intercept. There are three possible scenarios, which can occur when graphing parabolas, that determine if and how many x-intercepts exist:

1.    The graph of the parabola does not cross the x-axis and hence no x-intercepts exist (this happens when the vertex of the parabola lies above the x-axis and opens upward or when the vertex lies below the x-axis and opens downward).

2.    The graph crosses the x-axis at two points (when the parabola lies below the x-axis and opens upward or when the vertex lies above the x-axis and opens downward).

3.    The graph touches the x-axis at one point, which is also the vertex of the parabola (this happen when k = 0).

If the zeros of a function are real numbers, calculate the x-values when f(x) = 0.

### Tutorial Details

 Approximate Time 25 Minutes Pre-requisite Concepts Students should understand the concepts of axis of symmetry, evaluating functions, orientation of a quadratic function, parabola, quadratic, quadratic function in vertex form, solving linear equations vertex, x–intercept, y–intercept. Course Algebra-2 Type of Tutorial Procedural Development Key Vocabulary axis of symmetry, graph of a quadratic function, quadratic function in vertex form