Objective - To use the discriminant to determine
the number of real solutions for a quadratic.
Quadratic Formula
2
b  b  4ac
x
2a
Used to find the
roots of a quadratic
equation...
2
y  ax  bx  c
or
2
0  ax  bx  c
Discriminant
2
b  4ac
Used to find the
number of roots.
2
Two
real
b  4ac  0 roots
2
real
b  4ac  0 One
root
2
real
b  4ac  0 Noroots
Determine the number of roots for the quadratic
equation below.
2
y  2x  5x  3
a2
b  5
c3
2
b  4ac  0
5  423
2
25  24  1
Two Real Solutions
Determine the number of x-intercepts for the
quadratic equation below.
2
y  x  4x  7
a  1
b4
c  7
2
b  4ac  0
4   4 17
2
16  28  12
No Real Solution
Determine the number of x-intercepts for the
quadratic equation below.
2
y  x  6x  9
a 1
b  6
c9
2
b  4ac  0
6  419
2
36  36  0
One Real Solution
Match each equation below with its graph.
a)
b)
c)
2
b
___1)
y  2x  x 1
2
b  4ac
2
1  421
1 8  7
2
2
c
___2) y  x  x  2
b  4ac
2
1  412
18  9
2
2
a 3) y  x  2x 1 b  4ac
___
2
2  411
4 4  0
No Real
Roots
Two Real
Roots
One Real
Roots
Tell whether the vertex lies above, below, or on
the x-axis.
2
1) y  3x  2x  4
Opens up
2
b  4ac
2
2  434
4  48  44
No Real Roots
Vertex lies
Above x-axis
2
2) y  x  5x 1
Opens down
2
b  4ac
2
5  4 11
25  4  29
Two Real Roots
Vertex lies
Above x-axis