 Use of parabolas ◦ Projectiles ◦ Suspension bridges ◦ Parabolic lenses ◦ Satellite dishes ◦ Parabolic microphones.

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Presentation transcript:

 Use of parabolas ◦ Projectiles ◦ Suspension bridges ◦ Parabolic lenses ◦ Satellite dishes ◦ Parabolic microphones

 The graph of a quadratic function is called a parabola (not new to you)  Every quadratic equation yields a parabola, each parabola has an axis of symmetry. The line in which we can fold the graph and the left side lays on top of the right side.  The vertex of the parabola is the point where the axis of symmetry intersects the parabola. If a>0, the parabola is concave up, opens upward (could hold water)  If a<0, the parabola is concave down, opens down (water falls out)

 Parabolas that are concave down have maximum values.  Parabolas that are concave up have minimum values.  The bigger the |a| is the narrower the parabola is. Think of the following graphs.  The resulting y values in the 2 nd graph are 6 times larger than that of those in the first equation.

 The following equation will provide you with the x-value of the vertex. ◦ Once you know x, plug it into f(x) to get your y value of the vertex.

 When using the y intercept is always equal to c.  To find the x-intercepts solve for x. Your discriminant should tell you how many x-intercepts to expect.

 We can also find the vertex, axis of symmetry, x-intercepts, and y-intercepts through the use of completing the square.  When we are done doing that we will be left with something in the form of thus the vertex will be located at (h,k)

Do you know what the x coordinate of the vertex would be? Think about the x-intercepts and symmetry of parabolas. My names fay and I'm not smart at all.

 You do not have to graph these.