Alg2 SumSch Quad Quiz1

Answer explanation

The correct roots of the quadratic equation x^2 - 5x + 6 = 0 are x = 2 and x = 3, as they satisfy the equation when substituted back in.

Answer explanation

The vertex of a parabola in the form y = ax^2 + bx + c is given by (-b/2a, c). In this case, the vertex is (2, 0) since a = 1, b = -4, and c = 4.

• Upward

• Downward

• Leftward

• Rightward

Answer explanation

The correct direction of the parabola is downward because the coefficient of the x^2 term is negative, indicating a downward opening parabola.

Answer explanation

To solve the quadratic equation 2x^2 - 4x - 6 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. Plugging in a=2, b=-4, and c=-6, we get x = 3 and x = -1 as the solutions.

• 1 second

• 2 seconds

• 3 seconds

• 4 seconds

Answer explanation

The ball hits the ground when h = 0. Substituting h = 0 in the equation, we get -5t^2 + 20t + 5 = 0. Solving this quadratic equation, we find t = 3 seconds.

Answer explanation

The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by b^2 - 4ac. In this case, a = 3, b = -2, and c = 1. Substituting these values, we get (-2)^2 - 4*3*1 = 4 - 12 = -8. Therefore, the discriminant is -8.

Answer explanation

To solve the quadratic equation x^2 + 6x + 9 = 0, we factor it to (x + 3)^2 = 0. Solving for x gives x = -3.

Answer explanation

The vertex of the parabola is given by the formula x = -b / 2a. Substituting the values from the equation y = -2x^2 + 8x - 5, we get x = 2. Plugging x = 2 back into the equation gives y = 3. Therefore, the vertex is (2, 3).

Answer explanation

The vertex of the parabola is at (3, 0) which is the point where the parabola reaches its minimum or maximum value.

Answer explanation

To solve the quadratic equation x^2 + 4x + 4 = 0, we apply the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. Plugging in a=1, b=4, and c=4, we get x = (-4 ± √(4 - 16)) / 2. Simplifying gives x = -2.