Solving Quadratics
Solve for x: x² = 9
x = ±3
If (x - 4)(x + 2) = 0, what are the solutions of x?
4 and -2
Factor x² - 16
(x - 4)(x + 4)
Complete the square: x² + 6x + ?
9
A ball is tossed upward with height given by h = -16t² + 32t. When does it hit the ground?
0 or 2 seconds
Solve for x:
x² + 5x = 0
0 and -5
State the zero product property.
If ab=0 then a = 0 or b = 0
Factor x² + 6x + 9
(x + 3)(x + 3)
Solve by completing the square: x² + 4x + 1 = 0
x = -2 ± √3
The product of two consecutive integers is 56. Write an equation to represent this.
x(x + 1) = 56
Solve for x:
x² - 3x - 4 = 0
4 and -1
Solve for x:
(2x - 1)(x + 3) = 0
1/2 and -3
Factor 2x² + 7x + 3
(2x + 1)(x + 3)
State the quadratic formula.
x = (-b ± √b² - 4ac)/2a
A rectangle has area 30m² and length x + 5 meters, width x meters. Write and solve a quadratic equation for x.
x(x + 5) = 30 x = 5 and x = -6
Solve for x:
2x² + 4x - 6 = 0
1 and -3
Solve for x:
(x + 5)² = 0
-5
Factor: 3x² - 12x + 12
3(x - 2)²
Use the quadratic formula to solve x² - 2x - 8 = 0
4 and -2
A quadratic equation has no real solutions. What does this mean about its graph?
The parabola does not cross the x-axis
Solve for x:
x² + 5x + 6 = 0
-2 and -3
If (x - 7)(x + 4) = 10, can you use the zero product property ?
Factor: 4x² - 25
(2x - 5)(2x + 5)
Use the quadratic formula to solve 3x² + 3x - 10 = 0
(-3 ± √129) / 6
A toy rocket is launched with height h = -5t² + 20t + 15. When will it hit the ground?
5 seconds (-0.6 does not make sense as a solution)