Discriminant
Determine the number of real solutions for x2 + 4x + 4 = 0
1 real solution (discriminant=0)
solve: x2 + 5x + 6 = 0
x = -2, x= -3
Solve: x2 - 4x - 5 = 0
x = 5, x = -1
find the vertex of:
y = x2 - 4x + 1
( 2 , -3 )
Solve: x2 = 49
x = 7, x = -7
Determine the number of real solutions for 2x2 - 3x + 5 = 0
No real solutions (Discriminant=-31)
solve x2 - 9 = 0
x = 3, x = -3
solve: x2 + 2x - 8 = 0
x = -4, x = 2
find the vertex of:
y = x2 + 6x + 5
( -3 , -4 )
Solve: (x - 2)2 = 16
x = 6, x = -2
Determine the number of real solutions for x2 - 7x + 10 = 0
2 real solutions (discriminant=9)
Solve: x2 - 11x + 24 = 0
x = 8, x = 3
solve: 2x2 + 3x - 2 = 0
x = -2, x = 1/2 (or x = 0.5)
find the vertex of:
y = 2x2 - 8x + 3
( 2 , -5 )
Solve: 3x2 = 75
x = 5, x = -5
Find the discriminant of
3x2 + 8x - 2 = 0
discriminant = 88
solve: 3x2 - 15x = 0
x = 0, x = 5
solve: 3x2 - 2x - 1 = 0
x = 1, x = -1/3 (or -0.333)
find the vertex of:
y = -x2 + 10x - 16
( 5 , 9 )
Solve: (x + 5)2 = 81
x = 4, x = -14
Determine the number of real solutions for
4x2 + 12x + 9 = 0
1 real solution (discriminant=0)
solve 2x2 + 7x + 3 = 0
x = -3, x = -1/2 (or x = -0.5)
Solve: 5x2 + x - 6 = 0
x = 1, x = -6/5 (or -1.2)
find the vertex of:
y = 3x2 + 12x + 7
( -2 , -5 )
Solve: 2(x - 1)2 - 50 = 0
x = 6, x = -4