Discriminant Activity
Question: How is the discriminant used to determine the number and type of solutions to a quadratic
equation?
Launch: Students will be given a half-sheet of paper with 5 quadratic equations that are not in standard
form. Students will have to match the a, b and c values to the correct quadratic equation. Students will
have 2 minutes to check with a partner and problem solve if there are discrepancies.
Investigation:
Discovering the Importance of the Discriminant Activity
FUNCTION
a
b
c
Discriminant
b  4ac
2
y  x2  6 x  5
y  2 x 2  11
y  x2  6x  9
y  3x 2  8
y  3x 2  12 x  8
Sketch of Graph
# of times
the graph
crosses or
touches the
x-axis
# of real
solutions
# of imag
solutions
y  3x 2  x  5
y  x 2  10 x  25
y  4 x 2  8 x  13
FUNCTION
a
b
c
Sketch of Graph
Discriminant
b 2  4ac
# of times
the graph
crosses or
touches the
x-axis
# of real
solutions
# of imag
solutions
y  5x2  8x
y  x 2  12
Conclusions/Closure: On a separate sheet of paper, answer the following:
Make a general statement about the value of the discriminant and what type of solutions a quadratic
has.