Daily Warm Up Determine the vertex and axis of symmetry:

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Presentation transcript:

Daily Warm Up Determine the vertex and axis of symmetry:

Focus of a Parabola (Section 2.3) Definition: A parabola can also be defined as the set of all points (x,y) in a plane that are equidistant from a fixed point called the focus and a fixed line called the directrix. The axis of symmetry contains the focus and is perpendicular to the directrix!

Focus of a Parabola … continued … Using the Distance Formula: d= We could take the distance between two points that are equidistant, but it would turn out like: Simply put, if your vertex is on the origin, your equation will be in the form: … where p is the distance from the vertex to the focus and –p is the distance from the vertex to the directrix.

Core Concepts

Core Concepts

Core Concepts

Core Concepts

Core Concepts Note The equation that we are using is almost identical to the vertex form of a quadratic . The one difference is that instead of using a, it is replaced with…

Focus of a Parabola … continued … Example 2: Example 3:

Focus of a Parabola … continued … Homework Help . . . 45) Identify the vertex, focus, directrix, and axis of symmetry for the following equation. Describe the transformations of the graph of the standard equation with p = 1 and vertex (0,0).