Lesson 6 – Creating a Quadratic Model from Data
Example:
A ball is thrown into the air from the top of a building. The table of values
gives the height of the ball at different times during its flight.
Time (s)
0
1
2
3
4
5
a)
Height (m)
30
50
60
60
50
30
Create a scatter plot, with an appropriate scale, from the data.
h
t
b)
Draw a curve of best fit. What shape best describes the graph?
c)
Extend the graph to estimate the location of the zeros.
d)
Use the zeros to write the equation in factored form.
[ HINT: substitute values for r and s in y = a (x – r)(x – s) ]
e)
In what direction does the parabola open? What does this tell you about the
value of a ?
f)
Using the y-intercept of the graph, calculate the value of a.
g)
Write the equation for the data in factored form.
[ HINT: substitute values for a, r and s in y = a (x – r)(x – s) ]
h)
Write the equation for the data in standard form.
Homework: p.177–178 # 3, 4ab, 7