Notes – Lesson 5.1
Algebra 2
Name __________________________________
1. Standard Form of a Quadratic Function.
f(x) = _________________________________________________
Examples: Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.
a. y = (2x + 3)(x – 4)
b. f(x) = 3(x2 – 2x) – 3(x2 – 2)
c. f(x) = (x2 + 5x – x2
d. f(x) = x(x + 3)
2. Graphing a Quadratic Function.
Definitions:
-parabola _________________________________________________
-axis of symmetry _____________________________________________________________________________
_____________________________________________________________________________
-vertex _____________________________________________________________________________________
The axis of symmetry of the graph of a quadratic function is always a _________________________________ defined by the
______________________________ of the ___________________. Two corresponding points are the __________________
______________________________ from the axis of symmetry.
Examples:
10
9
Vertex: _______________
8
7
6
Axis of Symmetry: ______________
5
4
Plot P(1, 2). Name corresponding point. ___________
3
2
Plot Q(0, 8) Name corresponding point. ___________
1
-1
1
-1
2
3
4
5
6
7
8
4
3
Vertex: _______________
2
1
Axis of Symmetry: ______________
-4
-3
-2
-1
1
2
3
4
-1
Plot P(-1, 3). Name corresponding point. ___________
-2
Plot Q(2, 0) Name corresponding point. ___________
-3
-4
3. Fitting a Quadratic Function to 3 Points.
Write a quadratic function that goes through these 3 points.
x
2
3
4
y
3
13
29
4. Calculator Steps.
The table below show the height of a column of water as it drains from its container. Model the data with a quadratic
function. Graph the data and the function. Use the model to estimate the water level at 35 seconds.
Elapsed
Time
0s
10 s
20 s
30 s
40 s
50 s
60 s
Water
Level
120 mm
100 mm
83 mm
66 mm
50 mm
37 mm
28 mm
1. Enter lists.
2. STAT – CALC - #5 – ENTER
3. Go to y =
4. VARS - #5 – EQ – ENTER
5. Go to 2nd Table and enter amount looking for.
5. A Function and a Given Point.
The graph of each function contains the given point. Find the value of c.
a.
y = x2 + c; (0, 3)
b.
y = -5x2 + c; (2, -14)
c.
y=
3
4
x2 + c; (3,
1
2
)