Curved Graphs

Curved Graphs

Plotting Parabola

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

Multiple Choice

What will the form of the parabola y = -2x² be?

• Concave up

• Concave down

Multiple Choice

What will the form of the parabola y = 3 - 2x² be?

• Concave up

• Concave down

Multiple Choice

What will the form of the parabola y = -3 + 2x² be?

• Concave up

• Concave down

Multiple Choice

Which of the following is the equation of the given parabola?

• y = 4x²

• y = x² + 4

• y = x² - 4

Multiple Choice

If graph f is y = x², what will the graph of g (red curve) be?

• y = 3x²

• y= - 1/3 x²

• y = 1/3 x²

Multiple Choice

If graph f is y = x², what will the graph of g (red curve) be?

• y = 3x²

• y= - 3x²

• y = 1/3 x²

Multiple Choice

Which of the following is true about the graph?

• maximum = -4

• minimum = -4

Multiple Choice

Which of the following is true about the graph?

• y-intercept = -4

• y-intercept = -2 and 2

Multiple Choice

Which of the following is true about the graph?

• vertex = (-4,0)

• vertex = (0, -4)

• vertex= (0,-2)

Multiple Choice

Which of the following is true about the graph?

• it has ONLY one x-intercept

• y-intercept = 4

• x-intercept = -2 and 2