Objectives

• Construct a table of values for quadratic

• Plot the graph of a parabola from a table of values

What is a parabola?

• A parabola is a smooth U-shaped curve. 

• An equation of the form y = ax² + bx + c will graph to give a parabola.

• This lesson concentrates on parabolas of the form y = ax² + c.

Read the equation of a parabola

• You can draw a quick sketch of a parabola using the information from its equation, y = ax² + c.

• The coefficient of x², a, tells you the DIRECTION and WIDTH of the parabola.

Read the equation of a parabola

• You can draw a quick sketch of a parabola using the information from its equation, y = ax² + c.

• The constant value, c, in the equation of a parabola, tells you the y-intercept. Changing the constant term c moves the curve up or down the axis.

The axis of symmetry and vertex

• The axis of symmetry is the line along which the graph can be folded so that both halves of the parabola overlap.

• The vertex is the point at which the parabola turns.

• For y = ax² + c, the axis of symmetry is the y-axis (x = 0)

• For y = ax² + c, the vertex is the y-intercept (0,c).

The domain and range

• The domain represents the possible x values of the parabola and the range gives the possible y values

• For the parabola y = x² + 2:

• the domain is: all real values of x

• the range is: y ≥ 2

Describing a parabola (1)

• Concave up

• x-intercepts = –8 and 8 y-intercept = –1

• Minimum = –1

• Domain: all real x Range: y ≥ –1

• Vertex: (0, –1)

Describing a parabola (2)

• Concave down

• x-intercepts = –5 and 5 y-intercept = 7

• Maximum = 7

• Domain: all real x Range: y ≤ 7

• Vertex: (0, 7)

Describing a parabola (3)

• Concave up

• No x-intercepts , y-intercept = 2

• Minimum = 2

• Domain: all real x Range: y ≥ 2

• Vertex: (0, 2)

Describing a parabola (4)

• Concave down

• x-intercepts s = - V5 and V5, y-intercept = 5

• Maximum = 5

• Domain: all real x Range: y ≤ 5

• Vertex: (0, 5)

Ready for exercise???

The following slides contain questions from the previous slides you have learned. You may revise the slides before you go to next slides