Chapter 5
Graphs and Properties of Quadratic Functions in Standard Form
Investigative Activity
Graph the following function using the provided table of values:
f ( x) = x 2 + 2 x − 3
x
f(x)
-4
-3
-2
-1
0
1
2
3
Why isn’t the graph linear ?
Functions that have a degree of _____________ graph ______________
What is the minimum point on the parabola ? _________________
Standard Form: _______________ where a=____, b=_____, c=____
Vertex: ________________________________________
x =____________
f(x) = __________
Axis of Symmetry:_______________________
What is the y-intercept of the parabola.
What are the x-intercepts of the parabola ?
• How can we solve this using algebra and no table or graph to
find the x-intercepts ?
Chapter 5
Graphs and Properties of Quadratic Functions in Standard Form
GRAPH:
f ( x) = 2 x 2 − 8 x + 6
Steps for graphing quadratic equations:
 − b  − b 
1.) Find the vertex 
, f
 
 2a  2a  
2.) Find x-values equidistant from the x-coordinate of the vertex.
vertex
x
f(x)
Follow Up Questions:
• Is the quadratic equation in standard form ?
a=____ b=____ c=_____
• Why does this function graph a parabola ?
• What is “a” in this problem ? How did that change the graph ?
•
•
What is the axis of symmetry ?
What is the y-intercept ? How can you find that algebraically ?
•
How can you find the x-intercepts of this graph algebraically?
Chapter 5
Graphs and Properties of Quadratic Functions in Standard Form
GRAPH:
f ( x) = −
−b
,
1.) Find the vertex 
 2a
1 2
x +4
2
 − b 
f
 
 2a  
2.) Find x-values equidistant from the x-coordinate of the vertex.
vertex
x
f(x)
Follow Up Questions:
•
•
a=____ b=____ c=_____
Why does this function graph a parabola ?
What is the value of a ? How did this change the graph ?
•
•
What is the axis of symmetry ?
What is the y-intercept ? How can you find that algebraically ?
•
How can you find the x-intercepts of this graph algebraically?
Method 1 :
Method 2 (can only use when b = 0):
Chapter 5
Graphs and Properties of Quadratic Functions in Standard Form
f ( x) = − x 2 + 2 x − 1
Ex.1
What is the value of a ? How did this change the graph ?
What is the vertex ?
Find the x-intercept(s).
Use the vertex and x-intercepts to sketch a graph of the function.
Ex. 2
f ( x ) = −3 x 2 + 27
What is the vertex ?
What is the value of b ?
Find the x-intercepts (note b=0).
• Method 1:
•
Method 2:
Use the vertex and x-intercepts to sketch a graph of the function.
Chapter 5
Graphs and Properties of Quadratic Functions in Standard Form
Ex. 3
f ( x ) = 2 x 2 − 16
What is the vertex ?
Find the x-intercepts (note b=0).
• Method 1:
•
Method 2:
Use the vertex and x-intercepts to sketch a graph of the function.
Ex. 4
f ( x) = x 2 + 4
 − b  − b 
, f
1.) Find the vertex 
 
 2a  2a  
2.) Find x-values equidistant from the x-coordinate of the vertex.
vertex
X
f(x)
What is unusual about this graph ?
Chapter 5
Graphs and Properties of Quadratic Functions in Standard Form
Chapter 5
Graphs and Properties of Quadratic Functions in Standard Form