(1) Graphing Quadratic Function in Standard form.notebook February 09, 2015
Lesson 11Graph Quadratic Functions in Standard Form
Objective: To graph quadratic functions
A QUADRATIC FUNCTION is a function that can be written in the form y = ax2 + bx + c. This is called the STANDARD FORM of a quadratic function.
Examples:y = 3x2 y = x2 + 9 y = x2 x 2
(1) Graphing Quadratic Function in Standard form.notebook February 09, 2015
The simplest quadratic function is y = x2
This is called the PARENT FUNCTION
The graph of a quadratic is a PARABOLA
The highest or lowest point is called the VERTEX
This is a minimum point because it is the lowest
This is a maximum point because it is
the highest
(1) Graphing Quadratic Function in Standard form.notebook February 09, 2015
vertex
vertex
The vertex is the lowest point of a parabola that opens up and the highest point of a parabola opens down.
The line passing through the vertex that divides the parabola into symmetric parts is called the axis of symmetry.
y = x2
y = x2
Graph the function y = x2. Make a table of values. What is the domain & range? Remember this is the parent function!
x y
Domain:
Range:
Compare to Parent:
(1) Graphing Quadratic Function in Standard form.notebook February 09, 2015
Problem 2: Graphing y = ax2Graph the function y = 2x2. Make a table of values. What is the domain & range? Compare with the graph y=x2
x y
Domain:
Range:
Compare to Parent:
Graph the function y = ½x2 +3 . What are the domain & range? Compare with the graph y=x2
x y
Domain:
Range:
Compare to Parent:
(1) Graphing Quadratic Function in Standard form.notebook February 09, 2015
Comparing Widths of ParabolasGraph the following & identify what changes each time.
A. y = 4x2
B. y = 1/4x2 +2
C. y = x2 5
Conclusion...
When we multiply a quadratic function by a whole number, the graph gets skinnier. When we multiply a quadratic function by a fraction, the graph gets wider.
(1) Graphing Quadratic Function in Standard form.notebook February 09, 2015
Problem 4: Graphing y = ax2 + cHow is the graph of y = 2x2 + 3 different from the graph of y = 2x2 ?
The graph of y = ax2 + bx + c is a parabola:
If a is positive, the parabola opens up.
If a is negative, the parabola opens down.
The vertex has an xcoordinate of
The axis of symmetry is the vertical line x =
The y interecpt is c. So the point (0, c) is on the parabola.
The graph is narrower than the graph of y= x2 if a is > 1 and wider if a is < 1
b2a
b2a
(1) Graphing Quadratic Function in Standard form.notebook February 09, 2015
To graph a quadratic function...
Step 1: Identify the coefficients of the function. The coefficients are a= 2, b= 8, c= 6. Because a>0, the parabola opens up.
Step 2: Find the vertex. First calculate the xcoordinate.
x=
Then, find the y coordinate of the vertex.
Step 3: Draw the axis of symmetry.
Step 4: Identify the yintercept c. Plot the point for the yintercept.
Step 5: Evaluate the function for other values of x.
Step 6: Draw the parabola through the plotted points.
Graph y = 2x2 8x + 6
b2a
Graph y = 2x2 8x + 6.
(1) Graphing Quadratic Function in Standard form.notebook February 09, 2015
Conclusion...
When we add a number to our parent function, the graph shifts up. When we subtract a number from our parent function, the graph shifts down.
Problem 5: Using the Falling Object ModelAn acorn drops from a tree branch 20 ft above the ground. The function h = 16t2 + 20 gives the height h of the acorn (in feet) after t seconds. What is the graph of this quadratic function? At about what time does the acorn hit the ground?
(1) Graphing Quadratic Function in Standard form.notebook February 09, 2015
Problem 1: Identifying a VertexWhat are the coordinates of the vertex of each graph? Is it a minimum or a maximum?
A.
B.