introduction to parabolas spi 3103.3.11 graph conic sections (circles, parabolas, ellipses and...

Introduction to ParabolasSPI 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.

Types of Conic Sections

• Parabola

• Circle

• Ellipse

• Hyperbola

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.

Important Information About Parabolas

• The vertex of a parabola is the ordered pair (h, k).

Vertex

Important Information About Parabolas

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

Axis of Symmetry

Important Information About Parabolas

• If a > 0, the parabola will open upward.

• If a < 0, the parabola will open downward.

Important Information About Parabolas

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

Important Information About Parabolas

• To find the y-intercept of a parabola, substitute 0 for x; then solve the equation for y.

Practice With Parabolas

Practice with Parabolas

For the following problems, give

a.) the vertex

b.) the axis of symmetry

c.) the direction the parabola

opens

Practice with Parabolas

1. y – 11 = 2(x + 7)2

2. y + 7 = –(x – 5)2

3. y = 5(x + 10)2

Practice with Parabolas

4. y – 7 = –8x2

5. y = 15x2

6. y = –x2