Solving by Factoring
Solve (x – 3)(x + 4) = 0 by factoring.
x =3 and -4
Completing the square is where we...
Transform ax2+bx+c = 0 into a(x+d)2 + e = 0 and solve for x
What is the Quadratic Formula?
x=(-b +/-√(b2-4ac))/2a where ax2+bx+c
Solve x2 - 4 = 0 by taking the square root.
x = +/-2
Describe the shift that occurs between F(x) = x2 and F(x) = x2 - 5 on a graph.
Shift down of 5 units
Solve x2 + 5x + 6 = 0
x = -3 and -2
Solve x2 + 6x – 7 = 0 by completing the square.
x = -7 and 1
What is the discriminant and what does it do?
The part of the quadratic formula that looks like (b2-4ac) that determines how many solutions there are to the given quadratic equation.
+ discriminant = two distinct real number solutions
discriminant of 0 = a repeated real number solution
- discriminant = zero real number solutions
Solve 2x2 + 3 = 131 by taking the square root.
x = +/-8
Describe the shift that occurs between F(x) = x2 and F(x) = (x - 5)2 on a graph.
Shift of 5 units right
Solve x2 – 3 = 2x
x = -1 and 3
Solve x2 + 4x + 1 = 0
x = +/-√3 - 2
How many solutions does 6x2 + 10x − 1 = 0 have?
Two
Solve 9x2 + 56 = 47 by taking the square root.
x = +/-i
Describe the shift that occurs between F(x) = x2 and F(x) = _x2 on a graph.
1) 2
2) 0.5
1) Stretches the graph vertically by a factor of 2
2) Compresses the graph vertically by a factor of 2
Solve (x + 2)(x + 3) = 12
x = -6 and 1
Solve 5x2 – 4x – 2 = 0
x = +/-√0.56 +.04
What are the solutions to x2 - 10x + 20 = 0
x = 5 +/-√5
Solve x2 - 50 = 0 by taking the square root.
x = +/-5√2
Describe the shift that occurs between F(x) = x2 and F(x) = -x2 on a graph.
It flips the parabola upside-down
Solve:
1) x2 + 5x = 0
2) x2 – 4 = 0
1) x = 0 and -5
2) x = -2 and 2
Solve x2 + 10 = –6x
x = -3 +/-i
What are the solutions to 2x2 - 2x - 5 = 0
(1 +/-√11)/2
Solve ___ by taking the square root.
1) (x - 5)2 - 100 = 0
2) (x - 2)2 - 12 = 0
!) x = -5 and 15
2) 2 +/-2√3
Describe the shifts that occurs between F(x) = x2 and F(x) = -(1/3)(x+9)2+6 on a graph.
The parabola flips upside-down, is vertically compressed by a factor of 3, and is shifted 9 units left and 6 units up.