Quadratic Functions IQ Analysis Questions

• All real numbers that are greater than or equal to 0 and less than or equal to 30

• All real numbers that are greater than or equal to 0 and less than or equal to 60

• All real numbers that are greater than or equal to 900

• All real numbers that are less than or equal to 900

Answer explanation

The function f(x) = -x^2 + 60x is a downward-opening parabola. Its maximum value occurs at the vertex, which is 900. Thus, the range is all real numbers less than or equal to 900.

A part of quadratic function g is graphed on the grid. What is the domain of the part of the function shown?

• All real numbers greater than or equal to -4 and less than or equal to 5

• All real numbers greater than or equal to -1 and less than or equal to 3

• All real numbers greater than or equal to -6 and less than or equal to 6

• All real numbers greater than or equal to -2 and less than or equal to 3

Answer explanation

The graph shows the part of the quadratic function between x = -2 and x = 3. Therefore, the domain is all real numbers from -2 to 3, inclusive.

• The domain of the function is x ≥ 2.

• The range of the function is n(x) ≥ -8.

• The domain of the function is x ≥ 0.

• The range of the function is n(x) ≤ 12.

Answer explanation

The function n(x) = 5x^2 - 20x + 12 is a quadratic with a minimum value. Completing the square shows the vertex is at (2, -8), indicating the range is n(x) ≥ -8, making this statement true.

Which graph best represents part of a quadratic function with a domain of all real numbers less than -4?

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What is the range of h?

• All real numbers

• All real numbers greater than or equal to -7

• All real numbers greater than or equal to -8

• All real numbers greater than or equal to 0

Answer explanation

The range of h is determined by its minimum value. Since the correct answer is 'All real numbers greater than or equal to -8', it indicates that h can take any value starting from -8 and above.

Which quadratic function in vertex form can be represented by the graph that has a vertex at (1, 46) and passes through the point (3, 10)?

Answer explanation

The vertex form is y = a(x - h)^2 + k. Here, (h, k) = (1, 46). To find 'a', use the point (3, 10): 10 = a(3 - 1)^2 + 46. Solving gives a = -9. Thus, the function is y = -9(x - 1)^2 + 46.

Answer explanation

To find the equivalent function, expand f(x) = -4(x + 7)^2 - 6. This gives f(x) = -4(x^2 + 14x + 49) - 6 = -4x^2 - 56x - 196 - 6 = -4x^2 - 56x - 202. Thus, the correct choice is f(x) = -4x^2 - 56x - 202.

The graph shows the height in feet of an object above the ground t seconds after it was launched from the ground. Which function is best represented by the graph of this situation?

Answer explanation

The correct function, h(t) = -16t^2 + 64t, represents a projectile motion with an initial upward velocity (64t) and a downward acceleration due to gravity (-16t^2). This matches the graph's shape and behavior.

The graph of a quadratic function is shown on the grid. Which function is best represented by this graph?

Answer explanation

The graph opens downward, indicating a negative leading coefficient. The correct function, f(x) = -x^2 - 3x + 4, matches this behavior and the vertex position, confirming it as the best representation of the graph.

The graph of a quadratic function is shown. Which values best represent the zeros of the function? Select TWO correct answers.

• A) x = 1

• B) x = -3

• E) x = 0

• D) x = 3

• C) x = -1

Answer explanation

The zeros of the quadratic function are the x-values where the graph intersects the x-axis. From the graph, the function crosses at x = 3 and x = -1, making D) x = 3 and C) x = -1 the correct answers.