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Introduction to Parabolas SPI 3103.3.11 Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the standard form and the key characteristics of the graph.

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Types of Conic Sections Parabola Circle Ellipse Hyperbola

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Equation of a Parabola The general form for the equation of a parabola is y – k = a(x – h) 2. The equation may also be written in the form y = a(x – h) 2 + k.

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Important Information About Parabolas The vertex of a parabola is the ordered pair (h, k). Vertex

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Important Information About Parabolas The axis of symmetry (axis) is the line x = h. Axis of Symmetry

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Important Information About Parabolas If a > 0, the parabola will open upward. If a < 0, the parabola will open downward.

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Important Information About Parabolas The larger a, the narrower the parabola will be.

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Important Information About Parabolas To find the y-intercept of a parabola, substitute 0 for x; then solve the equation for y.

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Practice With Parabolas

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Practice with Parabolas For the following problems, give a.) the vertex b.) the axis of symmetry c.) the direction the parabola opens

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Practice with Parabolas 1. y – 11 = 2(x + 7) 2 2. y + 7 = –(x – 5) 2 3. y = 5(x + 10) 2

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Practice with Parabolas 4. y – 7 = –8x 2 5. y = 15x 2 6. y = –x 2

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