5.1 Modeling Data with Quadratic
Functions
Quadratic Functions
Standard Form of a Quadratic Equation:
f(x) =
ax2
quadratic term
+
bx
+
linear term
c
a≠0
constant term
Ex 1) Are the following functions quadratic or linear?
a. y = (2x + 3)(x - 4)
b. f(x) = 3(x2 - 2x) - 3(x2 - 2)
Parabolas
Parabola: the graph of a quadratic function
Axis of Symmetry: the line that divides the parabola into two parts
that are symmetric (mirror images)
Vertex: the point where the parabola intersects the axis of symmetry
*the y-value of the vertex is the maximum or minimum value of the
function
Parabolas
Ex 2) Identify the vertex of each graph. Is it a
maximum or a minimum? Also, identify the points
that are symmetric to P and Q.
Finding a Quadratic from 3 Points
Ex 3) Find the quadratic equation that goes through the points
(2, 3), (3, 13), and (4, 29).
*We need to find a, b, and c…
System of 3 equations:
Now try this! – Quadratic Regression
Ex 4) The chart below tells us the height of water in mm as it drains
from a container over time in seconds. Find the equation of the parabola
that best fits this data (use calculator).
Time (s)
Height (mm)
0
120
10
100
20
83
30
66
40
50
50
37
60
28
HW: 5.1 p. 241 #1-21 odd, 27-29 all, 32, 33
5.1 Modeling Data with Quadratic
Functions