Transcript 2.10 Graph y = ax2 + c - Brookwood High School
2.10
Graph y = ax
2
+ c
2.10-2.11 Quiz: Friday Midterm: March 11
Vocabulary
• A
quadratic function
is a nonlinear (not a line) function that can be written in the standard form
y = ax 2 + bx + c
where a ≠ 0 • Every quadratic function has a
U-shaped
graph called a
parabola
.
Vocabulary
• The
most basic
quadratic function in the family of quadratic functions, called the
parent quadratic function
, is
y = x 2
X -2 Y = 4 -1 1 0 0 1 1 2 4
Parts of a Parabola
• The lowest or highest point on a parabola is the
vertex
. • The line that passes through the vertex and divides the parabola into two symmetric parts is called the
axis of symmetry
.
Graph y = ax
2 • The coefficient “a” can stretch or shrink the graph.
• If “a” is negative then the graph flips upside down. (Or as I like to call it…makes a SAD face)
Example 1:
• Graph y = 2x 2 . Compare the graph with the parent function, y = x 2 .
– You need to make a table of values. X Y = -2 -1 0 1 2
You Try:
• Graph y = 1/2x 2 . Compare the graph with the parent function, y = x 2 .
X -2 -1 0 1 2 Y =
Example 2:
• Graph y = -3x 2 . Compare the graph with the parent function, y = x 2 . – You need to make a table of values. X Y = -2 -1 0 1 2
Graph y = ax
2
+ c
• The constant “c” moves the graph up or down.
– If “c” is positive it moves the graph up – if “c” is negative it moves the graph down.
Example 4:
• Graph y = x 2 + 2. Compare the graph with the parent function, y = x 2 . – You need to make a table of values. X -2 -1 0 1 2 Y =
You Try:
• Graph y = x 2 – 4. Compare the graph with the parent function, y = x 2 .
Homework:
• P. 100 # 1-9all, 16, 17, 20, 21