1. y = ax + c
2

2. Vocabulary
 Quadratic Function – nonlinear function that can be
written in the standard form y = ax 2 + bx + c where a¹0
 Parabola – the U-shaped graph of any quadratic
function.

3. Graph of y = x 2
vertex axis
of symmetry

4. Example 1 Graph y = ax2 where | a | > 1
Graph y = 3x2. Compare the graph with the graph of
y = x2.
SOLUTION
STEP 1 Make a table of values for y = 3x 2.
x –2 –1 0 1 2
y 12 3 0 3 12
STEP 2 Plot the points from the table.
STEP 3 Draw a smooth curve through the points.

5. Example 1 Graph y = ax2 where | a | > 1
STEP 4 Compare the graphs of y = 3x2 and y = x2.
Both graphs open up and have the same
vertex, (0, 0 ), and axis of symmetry, x = 0.
The graph of y = 3x2 is narrower than the
graph of y = x2.

6. Example 2 Graph y = ax2 where | a | < 1
1 2
Graph y = – x . Compare the graph with the graph of
y = x2. 4
SOLUTION
1 2
STEP 1 Make a table of values for y = – x .
4
x –4 –2 0 2 4
y –4 –1 0 –1 –4
STEP 2 Plot the points from the table.
STEP 3 Draw a smooth curve through the points.

7. Example 2 Graph y = ax2 where | a | < 1
1
STEP 4 Compare the graphs of y = – x 2 and y = x 2.
4
Both graphs have the same vertex, ( 0, 0 ), and
the same axis of symmetry, x = 0. However,
1 2
the graph of y = – x is a reflection in the
4 1
x-axis of the graph of y = x 2 and is wider than
4
the graph of y = x2.

8. Example 3 Graph y = x2 + c
Graph y = x2 + 5 . Compare the graph with the graph of
y = x2 .
SOLUTION
STEP 1 Make a table of values for y = x2 + 5.
x –2 –1 0 1 2
y 9 6 5 6 9
STEP 2 Plot the points from the table.
STEP 3 Draw a smooth curve through the points.

9. Example 3 Graph y = x2 + c
STEP 4 Compare the graphs of y = x2 + 5 and y = x2.
Both graphs open up and have the same axis
of symmetry, x = 0. However, the vertex of
the graph of y = x2 + 5 , ( 0, 5 ), is different
than the vertex of the graph of y = x2, ( 0, 0 )
because the graph of y = x 2 + 5 is a vertical
translation (of 5 units up) of the graph of y = x 2.

10. Example 4 Graph y = ax2 + c
1
Graph y = x2 – 4. Compare the graph with the graph of
2
y = x2.
SOLUTION
1
STEP 1 Make a table of values for y = x2 – 4.
2
x –4 –2 0 2 4
y 4 –2 –4 –2 4
STEP 2 Plot the points from the table.
STEP 3 Draw a smooth curve through the points.

11. Example 4 Graph y = ax2 + c
1
STEP 4 Compare the graphs of y = x2 – 4and y = x2.
2
Both graphs open up and have the same axis of
symmetry, .
x = 0 However, the graph of
1
y = x2 – 4 is a vertical translation (of 4 units
2 1
down) of the graph of y = x2
and is wider
2
than the graph of y = x 2.

13. 10.1 Warm-Up (Day 1)
Graph the function. Compare the graph with the graph
of y = x .
2
1. y = -4x 2
1 2
2. y = x
3
3. y = x2 + 2

14. 10.1 Warm-Up (Day 2)
Graph the function. Compare the graph with the graph
of y = x .
2
1. y = 3x - 6
2
2. y = -5x 2 +1
3 2
3. y = x - 2
4