Section 9.1Graphing Quadratic

Functions

Standard 21.0 Students graph quadratic functions and know that their roots are the x-intercepts.

• quadratic function• parabola• minimum• maximum

• Graph quadratic functions.

• vertex• symmetry• axis of symmetry

• Find the equation of the axis of symmetry and the coordinates of the vertex of a parabola.

The graph of a quadratic function is called a parabola.

If a is positive, then the parabola opens upward.

If a is negative, then the parabola opens downward.

The graph of a quadratic function is called a parabola.

If a is positive, then the parabola opens upward.

If a is negative, then the parabola opens downward.

A wider parabola has a leading coefficient closer to 0.

A narrower parabola has a leading coefficient farther from 0.

The vertex is the point where the parabola changes direction. It can be either a maximum or a minimum. (x, y) or (h, k)

Graph Opens Upwards

Use a table of values to graph y = x2 – x – 2.Graph these ordered pairs and connect them with a smooth curve.

Answer:

The lowest point of a parabola is called the minimum.

A. ARCHERY The equation y = –x2 + 6x + 4 represents the height y of an arrow x seconds after it is shot into the area. Use a table of values to graph y = –x2 + 6x + 4.Graph these ordered pairs and connect them with a smooth curve.

Answer:

Graph Opens Downward

The highestpoint of a parabola is called the maximum.

Parabolas have symmetry.• Symmetrical figures are those in which each half of the figure matches the other exactly.• The line of symmetry cuts a parabola in half.• The equation for the line of symmetry is

Vertex and Axis of Symmetry

A. Consider the graph of y = –2x2 – 8x – 2. Write the equation of the axis of symmetry.In y = –2x2 – 8x – 2, a = –2 and b = –8.

Answer: The equation of the axis of symmetry is x = –2.

Equation for the axis of symmetry of a parabolaa = –2 and b = –8

Vertex and Axis of Symmetry

B. Consider the graph of y = –2x2 – 8x – 2. Find the coordinates of the vertex. (x, y)Since the equation of the axis of symmetry is x = –2 and the vertex lies on the axis, the x-coordinate for the vertex is –2.

Answer: The vertex is (–2, 6).

y = –2x2 – 8x – 2 Original equationy = –2(–2)2 – 8(–2) – 2 x = –2y = –8 + 16 – 2 Simplify.y = 6 Add.

Vertex and Axis of Symmetry

C. Consider the graph of y = –2x2 – 8x – 2. Identify the vertex as a maximum or minimum.

Answer: Since the coefficient of the x2 term is negative, the parabola opens downward and the vertex is a maximum point.

A. x = –6

B. x = 6

C. x = –1

D. x = 1

A. Consider the graph of y = 3x2 – 6x + 1. Write the equation of the axis of symmetry.

A. (–1, 10)

B. (1, –2)

C. (0, 1)

D. (–1, –8)

B. Consider the graph of y = 3x2 – 6x + 1. Find the coordinates of the vertex.

A. minimum

B. maximum

C. neither

D. cannot be determined

C. Consider the graph of y = 3x2 – 6x + 1. Identify the vertex as a maximum or minimum.

D. Consider the graph of y = 3x2 – 6x + 1. Graph the function.A. B.

C. D.

Match Equations and Graphs

Which is the graph of y = –x2 – 2x –2?

A B

C D

Homework Assignment #56

9.1 Skills Practice Sheet