'Parabola opens' diaporamas de présentation

Chapter 9

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Complex Numbers

Complex Numbers. Complex Numbers. The imaginary unit i is defined as. Example. Complex Numbers.

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Chapter 13

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College Algebra Fifth Edition James Stewart ? Lothar Redlin ? Saleem Watson

College Algebra Fifth Edition James Stewart ? Lothar Redlin ? Saleem Watson. Conic Sections. 9. Chapter Overview. Conic sections are the curves we get when we make a straight cut in a cone. For example, if a cone is cut horizontally, the cross section is a circle.

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Properties of Quadratic Functions in Standard Form

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5-2

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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

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Warm Up

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Solutions of the equation

Solutions of the equation y = x 2 are shown in the graph. Notice that the graph is not linear. The equation y = x 2 is a quadratic equation . A quadratic equation in two variables can be written in the form y = ax 2 + bx + c, where a, b, and c are real numbers and

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5-2

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9-1

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Chapter 10

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Parabola

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The Beginning of Chapter 8: Conic Sections (8.1a)

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The general equation for all conic sections is:

The general equation for all conic sections is:. Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0. where A, B, C, D, E and F represent constants.

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5-Minute Check on Activity 4-2

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Write the standard equation of a parabola and its axis of symmetry.

Objectives. Write the standard equation of a parabola and its axis of symmetry. Graph a parabola and identify its focus, directrix, and axis of symmetry. Vocabulary. directrix and focus of a parabola.

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The axis of symmetry is the vertical line which passes through the vertex.

x = h. ( h , k ). ( h , k ). x = h. 3.2 Properties of Quadratic Relations. y = ax 2 + bx + c a > 0. If the second difference is positive, the graph opens up and the graph opens down if the second difference is negative.

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Quadratic Functions

Quadratic Functions. The parent function is given as. The graph of a quadratic function is called a parabola. This is the parent graph of all quadratic functions. Quadratic Functions. (-3,9). (3,9). A table of values can be constructed from the graph as given to the right. x y. -3 9.

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