Quadratic Functions Worksheet Extraction

A graph of a quadratic function is shown. Which location best represents the y-intercept of the function? Select ONE correct answer.

• y-intercept is approximately at (0, −5)

• y-intercept is approximately at (0, −4)

• y-intercept is approximately at (0, −3)

• y-intercept is approximately at (0, −2)

Answer explanation

The y-intercept occurs where the graph crosses the y-axis, which is at x = 0. The graph shows this point at approximately (0, −3), making it the correct choice.

The graph of quadratic function f is shown on the grid. What is the y-intercept of the graph of f? Select ONE correct answer.

• −5

• −4

• 0

• 4

Answer explanation

The y-intercept of a quadratic function is the point where the graph crosses the y-axis. In this case, the graph intersects the y-axis at (0, 4), so the y-intercept is 4.

The graph of quadratic function r is shown on the grid. Which answer choice best represents the intercepts of the graph of r?

• x-intercept: (5, 0); y-intercepts: (0, 10) and (0, −2)

• x-intercepts: (0, −10) and (0, 2); y-intercept: (−5, 0)

• x-intercept: (0, 5); y-intercepts: (10, 0) and (−2, 0)

• x-intercepts: (−10, 0) and (2, 0); y-intercept: (0, −5)

Answer explanation

The correct choice identifies the x-intercepts at (−10, 0) and (2, 0), and the y-intercept at (0, −5), accurately reflecting the points where the graph crosses the axes.

The graph of quadratic function f is shown on the grid. Which equation represents the axis of symmetry of the graph of f?

• x = −5

• x = −3

• y = −7

• y = 2

Answer explanation

The axis of symmetry for a quadratic function is a vertical line that passes through the vertex. In this case, the correct equation is x = -5, indicating that the graph is symmetric around this line.

The graph of a quadratic function is shown on the grid. Which statement appears to be true? Select ONE correct answer.

• The function has 3 zeros.

• The maximum value of the function is 3.

• The vertex of the graph of the function is (4, 1).

• The equation of the axis of symmetry of the graph of the function is x = 1.

Answer explanation

The axis of symmetry for a quadratic function is a vertical line that passes through the vertex. Since the correct answer states x = 1, this indicates that the vertex is at (1, y), confirming the axis of symmetry.

Two characteristics of quadratic function p are given: The axis of symmetry of the graph of p is x = −3. Function p has exactly one zero. Based on this information, which graph could represent p?

• 
• 
• 
• 

Answer explanation

The axis of symmetry x = -3 indicates the vertex is at this line. Since p has exactly one zero, it must touch the x-axis at this point, making graph A the correct representation of p.

• I and II only

• I and III only

• II and III only

• I, II, and III

Answer explanation

All statements I, II, and III are supported by the graph of the quadratic function k. The x-intercept is at (-3, 0), the y-intercept is at (0, 9), and the axis of symmetry is x = -3, confirming the correct choice is I, II, and III.

The graph of a quadratic function is shown on a grid. Which equation best represents the axis of symmetry?

Answer explanation

The axis of symmetry for a quadratic function is a vertical line that passes through the vertex. In this case, the graph shows that the vertex is at x=2, making the correct equation for the axis of symmetry x=2.

Answer explanation

The function f(x)=x^{2}+4x+3 is a parabola that opens upwards. Its vertex is at (-2,-1), making the minimum value -1. Thus, the range is all real numbers greater than or equal to -1.

• 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.