1. Standard
MM2A3. Students will analyze quadratic functions in the forms f(x) = ax2 + bx + c
and f(x) = a(x – h)2 + k.
c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change

2. The graph of a quadratic equation is a PARABOLA.
MM2A3c c. Investigate and explain characteristics of quadratic functions
A quadratic function is a function that can be written in standard form:
y = ax2 + bx + c
where a is not equal to 0.
The graph of a quadratic equation is a PARABOLA.

3. MM2A3c c. Investigate and explain characteristics of quadratic functionsy x
Parent Quadratic Function:
f(x) = x2
Let’s graph it with a table of values!!
x f(x)
Now let’s describe it!!

4. The lowest or highest point on a parabola
MM2A3c c. Investigate and explain characteristics of quadratic functions
Let’s define!!
Vertex:
The lowest or highest point on a parabola
In our parent function example:
Vertex: (0,0)

5. In our parent function example:
MM2A3c c. Investigate and explain characteristics of quadratic functions
Axis of Symmetry:
An invisible vertical line that divides the parabola into mirror images and passes through the vertex. (x = ____)
In our parent function example:
x = 0

6. The set of all input (x) values of a relation
MM2A3c c. Investigate and explain characteristics of quadratic functions
Domain:
The set of all input (x) values of a relation
In our parent function example:
Domain = all real numbers or

7. The set of all output (y) values of a relation
MM2A3c c. Investigate and explain characteristics of quadratic functions
Range:
The set of all output (y) values of a relation
In our parent function example:
Range = or

8. Where the graph of a function crosses or touches the x-axis
MM2A3c c. Investigate and explain characteristics of quadratic functions
Zero(s):
Where f(x) = 0;
Where the graph of a function crosses or touches the x-axis
In our parent function example:
Zero:
x = 0

9. The minimum(s) and maximum(s) of a function on a certain interval.
MM2A3c c. Investigate and explain characteristics of quadratic functions
Extrema:
The minimum(s) and maximum(s) of a function on a certain interval.
The vertex’s y-coordinate is the:
MINIMUM value if a>0
MAXIMUM value if a<0
In our parent function example:
Extrema: Minimum at y = 0

10. Interval(s) of Increase: From left to right on a graph,
MM2A3c c. Investigate and explain characteristics of quadratic functions
Interval(s) of Increase:
From left to right on a graph,
where as x increases, f(x) increases
In our parent function example:
Int. of Increase =
x > 0 Or

11. Interval(s) of Decrease: From left to right on a graph,
MM2A3c c. Investigate and explain characteristics of quadratic functions
Interval(s) of Decrease:
From left to right on a graph,
where as x increases, f(x) decreases
In our parent function example:
Int. of Increase =
x < 0 Or

12. Point(s) where the function crosses or touches the x-axis
MM2A3c c. Investigate and explain characteristics of quadratic functions
X-intercept(s):
Point(s) where the function crosses or touches the x-axis
In our parent function example:
X-intercept:
x = 0

13. Point(s) where the function crosses or touches the y-axis
MM2A3c c. Investigate and explain characteristics of quadratic functions
Y-intercept(s):
Point(s) where the function crosses or touches the y-axis
In our parent function example:
y-intercept:
y = 0

14. MM2A3c c. Investigate and explain characteristics of quadratic functions
Average Rate of Change:
The slope of the line that passes through two given points on the function
In our parent function example:
On the interval:
* Point 1 = (0,0)
* Point 2 = (2,4)
The average rate of change is 2

15. Characteristics of Quadratic Functions
Homework:
Characteristics of Quadratic Functions
Practice Sheet
WRITE PROBLEMS and
SHOW WORK for credit!!