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Math 2
Discriminant Task MM2A4c
NAME____________________
Graphing Calculator directions for graphing a parabola:
Step 1:
Step 2:
Step 3:
Step 4:
Turn on your calculator.
Press the Y = button right below the calculator’s screen
Type in the function to be graphed
Press the GRAPH button
Sketch the graph of the following parabolas using the calculator. Don’t try to be exact. Show how the
parabola interacts with the x-axis.
1. y = x2 + 2x – 8
2. y = x2  2x +3
3. y = x2  4x + 4
4. y = 2x2  5x  4
5. y = 4x2 + 20x  25
6. x2 + 3x + 5
What do you observe about the graphs?____________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
Now we are going to calculate the discriminant of each function. The discriminant of a function will tell
the number of roots and the nature of the roots. A quadratic can have real or imaginary solutions. The
discriminant of y = ax2 + bx + c is found using the formula b2  4ac. Fill in the chart using the same
equations that were graphed on the front.
Quadratic function
Discriminant (b2  4ac)
Number of x-intercepts
1. y = x2 + 2x – 8
2. y = x2  2x +3
3. y = x2  4x + 4
4. y = 2x2  5x  4
5. y = 4x2 + 20x  25
6. y = x2 + 3x + 5
Based on the results form the table, we can conclude the following:
When D > 0, there is/are _______ x-intercept(s).
When D = 0, there is/are _______ x-intercept(s).
When D <0, there is/are _______ x-intercept(s).
When the discriminant is greater than or equal to zero, that the parabola has either one or two real
solutions. The x-intercepts are the solutions. When the discriminant is less than zero, then there are still
solutions even though the parabola does not intercept the x-axis. The solutions are imaginary numbers.
Every time the discriminant > 0, there are 2 x-intercepts and _________ real roots. These real roots are
either rational or irrational.
 To determine if the real roots are rational: the discriminant is a __________ ____________
___________.
 To determine if the real roots are irrational: the discriminant is positive but it is NOT a
___________ ___________.
Every time the discriminant = 0, there is 1 x-intercept and __________ real root(s). It is a ____________
root.
Every time the discriminant < 0, there are 0 x-intercepts and _________ real roots, instead there are
_________ imaginary conjugate roots.
Can you ever have 1 real root and 1 imaginary root for a quadratic equation?_______________________
Let’s put it all together:
Discriminant
# of x-intercepts Number of
solutions
Nature of the roots
D > 0 and a
perfect square
D > 0 not a
perfect square
D=0
D<0
Complete the chart:
#
Quadratic Equation
1
f ( x)  x 2  5 x  14
2
f ( x)  x 2  3x  2
3
f ( x)  x 2  6 x  58
4
f ( x)  4 x 2  12 x  9
5
f ( x)  x 2  9
6
f ( x)  3x 2  11x  4
7
f ( x)  8 x 2  4 x  5
8
f ( x)  7 x 2  2 x  9
9
f ( x)  25 x 2  20 x  4
10
f ( x)  5 x 2  3x  1
Discriminant
# of xintercepts
# of
solutions
Nature of the roots
Use the graph to describe the discriminant (hint use: D > 0, D = 0, D < 0), number of x-intercepts and the nature of
the roots for the equation graphed.
11.
12.
Discriminant: ______________________
Discriminant: ______________________
# of x-intercepts: ___________________
# of x-intercepts: ___________________
Nature of roots:_____________________
Nature of roots:_____________________
13.
14.
Discriminant: ______________________
Discriminant: ______________________
# of x-intercepts: ___________________
# of x-intercepts: ___________________
Nature of roots:_____________________
Nature of roots:_____________________