Download The Discriminant

Solving Quadratics SQ10
Discriminant
Name __________________________
Date _______________ Period ______
Notes
Quadratic equations have no solutions, 1 solution, or 2 solutions. Solutions are real rational, real
irrational or imaginary.
Identify the number of xintercepts in the graphs below.
A. y = x2 + 4x –5
B. y = x2 + 2
C. y = x2
6x + 9
D. y = x2  3x  7
The discriminant determines the number and type of solutions to a quadratic equation. The
discriminant is found using the expression b2  4ac. Look at the equations of the graphs above.
Identify a, b, and c. Find the discriminant for each of the equations.
A. a =
b=
c=
B. a =
b=
c=
C. a =
b=
c =
D. a =
b=
c=
Using your answers from above, fill in the chart to help you determine the number and type of
solutions for each of the three outcomes of the discriminant.
Calculate b2
Discriminant = 0
# of real solutions:
Type of solutions:
 4ac
Discriminant = negative #
# of real solutions:
Type of solutions:
Discriminant = positive #
# of real solutions:
Type of solutions:
When the discriminant is
Type of solutions:
When the discriminant is
NOTE: The quadratic equation needs to be written in standard form, y= ax2 + bx + c, before you
begin.
Updated 5/21/2008
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Solving Quadratics SQ10
Finding the Number of Roots by Calculating the Discriminant (b2  4ac)
Equation
Standard Form
9x2 + 6x = 8
9x2 + 6x – 8 = 0
a, b, and c
a = 9 b = 6 c= 8
6x2  13x = 6
a=
b=
c=
2x  1 = 8x2
a=
b=
c=
3x2 + 10 = 17x
a=
b=
c=
a2 + 4a = 3
a=
b=
c=
y2 + 12y + 36 = 0
a=
b=
c=
r2 + 25 = 0
a=
b=
c=
Updated 5/21/2008
Discriminant:
b2 – 4ac
Simplified
discriminant
Number
of real
solutions
Square root
of
discriminant
Type of
solution
36  4 (9)( 8)
324
2
18
Real,
Rational
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