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
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:
Chapter 5
Graphs and Properties of Quadratic Functions in Standard Form
Ex.1
f ( x) = ! x 2 + 2 x ! 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 two other points on the graph to sketch the function.
Ex. 2
f ( x) = !3 x 2 + 27
What is the vertex ?
What is the value of b ?
Find the x-intercepts
Method 1:
Use the vertex and x-intercepts
to sketch a graph of the function.
Method 2:
Chapter 5
Graphs and Properties of Quadratic Functions in Standard Form
Ex. 3
f ( x) = x 2 + 4
&'b
1.) Find the vertex $$
,
% 2a
& ' b ##
f$
! !!
% 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