Graphing Quadratic Functions

1
Graphing Quadratic Functions

• Lesson 9.3A
• Algebra 2

2
Quadratic Function

• The standard form of a quadratic function is
  written

where a?0
and a, b, and c are constants.
3
Sketching a Quadratic Function

• The graph of a quadratic function is a U-shaped
  curve called a parabola.
• If the leading coefficient a is positive, then
  the parabola opens up.
• If the leading coefficient a is negative, then
  the parabola opens down.

4
Minimum and Maximum

• If the vertex is the lowest point of the
  parabola, then it is a minimum.
• If the vertex is the highest point of the
  parabola, then it is a maximum.

5
Axis of Symmetry

• The line passing through the vertex that divides
  the parabola into two symmetric parts. The two
  parts are mirror images of each other
  (reflections) about the line of symmetry.

6
Graph of a Quadratic Function

• The graph of y ax2 bx c is a parabola.
• If a is positive, then the parabola opens up.
• If a is negative, then the parabola opens down.
• The vertex has an x-coordinate of
• The axis of symmetry is the
• vertical line

7
Graphing a Quadratic Function

1. Find the x-coordinate of the vertex.
2. Find the y-coordinate of the vertex by plugging
   the x-coordinate into the quadratic equation and
   solving for y.
3. Make a table of values, using the x-values to the
   left and to the right of the vertex.
4. Plot the points and connect them with a smooth
   curve to form a parabola.

Example y 2x2 3x 4
8
Example

• Sketch the graph of
• y -4x2 3x 2

End of Lesson
9
Using a Quadratic Model in a Real-Life Problem

• Lesson 9.3B
• Algebra 2

10
Using a Quadratic Modelp. 522, 65

• Path of the dolphin jumping out of the water

h -0.2d2 2d
h height out of the water, d horizontal
distance
Our plan The maximum height reached by the
dolphin is the y-coordinate of the vertex.
First, we need to find the x-coordinate of the
vertex, then plug that value into the original
quadratic equation to find the y-value.
11
Using a Quadratic Modelp. 522, 65

• h -0.2d2 2d

so, a -0.2, b 2
The dolphin reached a maximum height of 5 feet
out of the water.
12
p. 522, 66

• How far did the dolphin jump?
• Hint Remember that a parabola is a reflection
  about the line of symmetry

End of Lesson