Quadratic Equations Mastery

Factor the quadratic expression: 2x^2 + 7x + 3

• (2x + 1)(x + 2)

• (2x + 2)(x + 1)

• (2x + 3)(x + 1)

• (2x + 1)(x + 3)

Solve the quadratic equation by factoring: x^2 - 5x + 6 = 0

• x = 3, x = 5

• x = 2, x = 4

• x = 2, x = 3

• x = 1, x = 4

Find the roots of the quadratic equation using the quadratic formula: 3x^2 + 4x - 2 = 0

• x = (-4 + 2√10) / 3 and x = (-4 - 2√10) / 3

• x = (-4 + √10) / 6 and x = (-4 - √10) / 6

• x = (-4 + 2√10) / 6 and x = (-4 - 2√10) / 6

• x = (-4 + 2√2) / 6 and x = (-4 - 2√2) / 6

A ball is thrown into the air with an initial velocity of 30 m/s. The height of the ball at any time t can be modeled by the equation h(t) = -5t^2 + 30t + 10. How long does it take for the ball to hit the ground?

• 4 seconds

• 6 seconds

• 10 seconds

• 8 seconds

Factor the quadratic expression: x^2 + 6x + 9

• (x + 3)^2

• (x + 5)^2

• (x + 2)^2

• (x + 4)^2

Solve the quadratic equation by factoring: 2x^2 - 9x - 5 = 0

• x = -1/2, 5

• x = -1/2, -5

• x = 1/2, 5

• x = 1/2, -5

Find the roots of the quadratic equation using the quadratic formula: 4x^2 + 8x + 3 = 0

• The roots of the quadratic equation 4x^2 + 8x + 3 = 0 are x = -1/2 and x = -3/2.

• The roots are x = 1 and x = 3

• The roots are x = 0 and x = -3

• The roots are x = -2 and x = -1

A rectangular garden has a length that is 4 meters more than twice its width. If the area of the garden is 60 square meters, find the dimensions of the garden.

• Width: 6 meters, Length: 16 meters

• Width: 10 meters, Length: 8 meters

• Width: 5 meters, Length: 15 meters

• Width: 8 meters, Length: 12 meters

Factor the quadratic expression: 3x^2 - 12x + 12

• (x + 2)(3x - 6)

• (x - 2)(3x - 6)

• (x - 2)(3x + 6)

• (x - 3)(3x - 4)

Solve the quadratic equation by factoring: x^2 + 5x - 6 = 0

• x = -5, x = 4

• x = -4, x = 3

• x = -6, x = 1

• x = -3, x = 2