1. Quadratic Graphs and Their Properties.
Quadratic Functions.
What you’ll learn
To graph quadratic functions of the form
To identify the axis of symmetry, vertex, domain.
range and intercept(s) for a given parabola.
Quadratic function, Standard form,
Parent function, parabola,
axis of symmetry, vertex, minimum,
maximum
Vocabulary

2. Take a Note: A quadratic function is a function that
can be written in the form
This form is called the standard form of a quadratic
function.
Examples:
The simplest quadratic function is
the quadratic parent function.
The graph od the quadratic function is called parabola
and has a U shape. You can fold a parabola so that the
two sides match exactly. The fold or line that divides
the parabola into matching halves is called the
axis of symmetry.

3. Problem 1: Graphing a Quadratic. Identifying a vertex.
Step 1: Make a table. X -2 4 -1 1 2 3 9

4. Step 2: Plot the points a)(-2, 4) (-1,1) (0,0) (1,1) (2,4) b)(-2,-8)
(-1,-2)
(0,0)
(1,-2)
(2,-8)
c)(-2,5)
(-1,3.5)
(0,3)
(1,3.5)
(2,5)

5. Take a note: The highest or the lowest point of a parabola is a vertex, which is on the axis of symmetry

6. Your turn:
A child drops a pebble from a height of 30 ft above a lake. The function gives the height h of the pebble
(in feet) after t seconds. What is the graph of this quadratic
function? At about what time does the pebble hit the water?

7. . The graph of , where has the line as its axis of as symmetry .
Take a note: There is another way to graph a parabola
. The graph of , where has the line as its axis of as symmetry
The x-coordinate of the vertex is and the
y-coordinate of the vertex is You can
use the coordinates of the vertex, the axis of symmetry and the y-intercept (meaning when x=0)to help you graph a quadratic function.

8. Problem 3: What is the graph of ?
Step 1: Identify a, b, and c.
Step 2: find the vertex, remember the x-value is the
axis of symmetry.
Step 3: The y-intercept
Step 4: Find another point in the side as the vertex.

9. Your turn: Graph
Answer

10. Problem 4: A baseball is thrown into the air with an upward
velocity of 30ft/s. Its height h, in feet,
after t seconds is given by the function
.How long will take the ball to
reach its maximum height? What is the ball’s
maximum height? What is the range of the
function?
Answer

11. Your turn: During a halftime basketball game, a slingshot
launches T-shirts at the crowd. A T-shirt is launched with an
Initial velocity of 72ft/sec. The T-shirt is caught 35 ft.
above the court. How long will take the T-shirt to reach its
maximum height? What is the maximum height? What is the
range of the function that models the height of the T-shirt
over time?
Answer

12. Classwork odd Homework even
TB pgs exercises. 7-48
pgs exercises 7-33