Quadratic Functions: Mixed Practice

Answer explanation

To find the vertex of the quadratic function f(x) = x^2 - 4x + 3, use the vertex formula x = -b/2a. Here, a = 1 and b = -4, so x = 2. Substitute x back into the function to find f(2) = -1. Thus, the vertex is (2, -1).

Answer explanation

The axis of symmetry for a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b/(2a). Here, a = 2 and b = 8, so x = -8/(2*2) = -2. Thus, the correct answer is x = -2.

Answer explanation

The domain of a quadratic function is always all real numbers, as it can take any value of x. Therefore, the correct choice is (-∞, ∞).

Answer explanation

To find the range of f(x) = x^2 - 6x + 8, we complete the square: f(x) = (x-3)^2 - 1. The vertex is at (3, -1), and since it opens upwards, the range is [-1, ∞). Thus, the correct answer is [-1, ∞).

Answer explanation

To find the vertex of the quadratic function f(x) = -x^2 + 4x - 5, use the vertex formula x = -b/(2a). Here, a = -1 and b = 4, giving x = 2. Substitute x back into f(x) to find y: f(2) = -1. Thus, the vertex is (2, -1).

Answer explanation

The axis of symmetry for a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b/(2a). Here, a = 1 and b = 2, so x = -2/(2*1) = -1. Thus, the axis of symmetry is x = -1.

Answer explanation

The domain of a quadratic function is always all real numbers, as it can take any value of x. Therefore, the correct choice is (-∞, ∞).

• y ≤ 3

• y ≥ 3

• y ≤ 1

• y ≥ 1

Answer explanation

The quadratic function opens downwards (coefficient of x^2 is negative). The vertex, found at x = 1, gives the maximum value f(1) = 3. Thus, the range is all values less than or equal to 3: (-∞, 3].

Answer explanation

To find the vertex of the quadratic function f(x) = 3x^2 - 12x + 9, use the vertex formula x = -b/(2a). Here, a = 3 and b = -12, giving x = 2. Substitute x = 2 into f(x) to find f(2) = -3. Thus, the vertex is (2, -3).

Answer explanation

The axis of symmetry for a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b/(2a). Here, a = -1 and b = 6, so x = -6/(2*-1) = 3. Thus, the axis of symmetry is x = 3.