9.3 Graphing Quadratic Functions. Quadratic Functions Quadratic functions are functions written in...
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Transcript of 9.3 Graphing Quadratic Functions. Quadratic Functions Quadratic functions are functions written in...
9.3 Graphing Quadratic Functions
Quadratic Functions
Quadratic functions are functions written in the form
Every quadratic function has a U-shaped graph called a parabola.
2y ax bx c
Axis of Symmetry
Vertex
y = ax2 +bx + c When a>0, the parabola opens up. The vertex is the minimum point.
Positive a = smiley face
If the leading coefficient is positive, the parabola opens up, like a U.
Axis of Symmetry
Vertex
y = ax2 +bx + c When a<0, the parabola opens down. The vertex is the maximum point.
Negative a = Sad Face
If the leading coefficient is negative, the parabola opens down, like an upside-down U.
Parabolas
The lowest/highest point on a parabola is called the vertex.
The axis of symmetry is the line that runs through the vertex and divides the parabola in two symmetric parts.
The x-coordinate of the vertex, and the equation of the axis of symmetry will be the line
x = -b
2a
2y ax bx c
GRAPHING QUADRATIC EQUATIONS Make a table
Plot points and connect dots to make a smooth curve.
2y ax bx c
X Y
Quadratic Functions will be in the form
y = ax2 + bx + c or f(x) = ax2 + bx + c
The graph of a Quadratic Function will be a parabola.
y = x2
Use the table with the given values for x to find f(x). Then graph the function
X Y
-2
-1
0
1
2
y = 2x2
y = -2x2
Graph each function, and compare them to the graph of y = x2
y = 5x2
y = ¼ x2
X Y
-2 20
-1 5
0 0
1 5
2 20
X Y
-8 16
-4 4
0 0
4 4
8 16
y = x2
y = 5x2
y = ¼ x2
Do you notice any patterns here?
As the coefficient (a) of x2 gets larger, the graph gets narrower;And if the coefficient is less than 1, the graph is wide.
Homework
Section 9.3Page 521, # 5-10, and # 11,12,14,15,19
Plus, Box and Whisker Question on Handout (See page 375)BONUS: Do p. 378, #8-10,#15-17