Completing the Square
Complete the square:
y= x2 + 6x + 8
y = (x+3)2 - 1
What is the quadratic formula?
x = -b +- sqrt(b2 - 4ac) /(2a)
What is the discriminant formula?
b2-4ac
Complete the square:
y = x2 - 6x + 5
y = (x-3)2 - 4
Solve the following quadratic equation by using the quadratic formula:
x2 + 6x + 5 = 0
x = -1 x = -5
Determine the discriminant and how many real solutions there are.
x2+5x+2
17, two real solutions
Complete the square:
y = 5x2 - 10x - 24
y = 5 (x-1)2 - 29
Solve the following quadratic equation by using the quadratic formula:
x2 - 9x + 20 = 0
x = 5 x = 4
Determine the discriminant and how many real solutions there are
x2+2x+1=0
0, 1 real solution
Complete the square:
y = 3x2 + 30x +16
y = 3(x+5)2 - 59
Solve the following quadratic equation by using the quadratic formula:
2x2 + 9x + 4 = 0
x = -1/2 x = -4
9x2-2x+1=0
-32, 0 zero solutions
Complete the square:
y = 2x2 - 32x + 72
y = 2(x-8)2 - 56
Solve the following quadratic equation by using the quadratic formula:
4x2 - 17x - 15 = 0
x = 5 x = -3/4
Determine the discriminant and how many real solutions there are.
9x2-7x+4=0
-95, 0 real solutions