Introduction to Parabolas

1
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.

2
Types of Conic Sections

• Parabola
• Circle
• Ellipse
• Hyperbola

3
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
5
Important Information About Parabolas

• The axis of symmetry (axis) is the line x h.

Axis of Symmetry
6
Important Information About Parabolas

• If a gt 0, the parabola will open upward.
• If a lt 0, the parabola will open downward.

7
Important Information About Parabolas

• The larger a , the narrower the parabola will
  be.

8
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
10
Practice with Parabolas

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

11
Practice with Parabolas

• y 11 2(x 7)2
• y 7 (x 5)2
• y 5(x 10)2

12
Practice with Parabolas

• 4. y 7 8x2
• 5. y 15x2
• 6. y x2