Warm-Up #35
10/7/16
For the quadratic function f(x) = 2(x + 3)2 - 3,
1. Make a table of values and graph.
2. What is the vertex and axis of symmetry?
Standard Form of a Quadratic
Function
Section 4-2
10/7/16
3. State the domain and range.
4. What is the minimum or maximum value?
EQ: In the quadratic function f(x)= 2+ + , what key information
about the values of a, b, and c, provide about the graph?
Quadratic Functions
Quadratic Functions
The standard form of
quadratic functions is
f(x) = ax2 + bx + c, where
a ≠ 0.
f(x) = x2 - 2x + 2
What is the vertex?
(1, 1)
What is the axis of symmetry?
Ex. f(x) = x2 - 2x + 2
x
-2
-1
0
1
x=1
What is the y-intercept?
2
(0, 2)
y
What is the value of a, b, and c? a = 1, b = -2, c = 2
Standard Form of Quadratic Functions
Quadratic Functions
f(x) = 2x2 + 8x - 2
2
f(x) = ax + bx + c
Vertex
● x-coordinate is
● Find the y-coordinate by plugging
Axis of Symmetry:
Y-intercept: (0, c)
Find…
1. a, b, and c
into the function
Opens Upward: a > 0
Opens Downward: a < 0
2. vertex
3. axis of symmetry
4. y-intercept
5. domain and range
Warm-Up #36
10/10/16
1. Write a quadratic function to model
the graph to the right.
2. A baseball is hit so that its height
above ground is given by the equation
h = -16t2 + 96t + 4, where h is the
height in feet and t is the time in
seconds after it is hit.
How long does it take the baseball to reach its highest
point? How high will it go?
Converting Standard Form to Vertex Form
Example
y = -x2 + 4x - 5
1. Identify a and b.
2. Find the x-coordinate of the vertex.
3. Find the y-coordinate of the vertex by plugging
the x-value into the function.
4. Write in vertex form, f(x) = a(x - h)2 + k, by
substituting in a, h, and k.
Interpreting a Quadratic Graph
The New River Gorge Bridge in West Virginia is the world’s
largest steel single arch bridge. You can model the arch
with the function
y = -0.000498x2 + 0.847 x,
where x and y are in feet.
How high above the river
is the arch? How long is
the section of bridge
above the arch?
Quadratic Functions
f(x) = -x2 + 2x - 5
Find…
1. a, b, and c
2. vertex
3. axis of symmetry
4. y-intercept
5. domain and range
Converting Standard Form to Vertex Form
1. y = 2x2 + 10x + 7
y = 2(x + 2.5)2 - 5.5
2. y = x2 - 4x + 6
y = (x - 2)2 + 2
3. y = -2x2 + 8x + 3
y = -2(x - 2)2 + 11
Exit Ticket
What steps transform the graph y = x2 to y = -2(x + 1)2 + 3?
A. Reflect across the x-axis, stretch by the factor of 2,
translate 1 unit to the right and 3 units up.
B. Stretch by the factor of 2, translate 1 unit to the right
and 3 units up.
C. Reflect across the x-axis, translate 1 unit to the left and
3 units up.
D. Stretch by the factor of 2, reflect across the x-axis,
translate 1 unit to the left and 3 units up.