Quadratic Functions Key Features and Graphing

How do you find the vertex of a quadratic function in standard form?

• Find the y-intercept and use it as the vertex

• Substitute x = 0 into the equation

• Take the average of the x-intercepts

• Use the formula x = -b/2a to find the x-coordinate of the vertex

What is the axis of symmetry of a quadratic function?

• x = a/2b

• x = -b/2a

• x = -b/a

• x = -a/2b

How do you determine the direction of opening of a parabola for a given quadratic function?

• By looking at the constant term in the quadratic function

• By examining the coefficient of the linear term in the quadratic function

• By counting the number of x-intercepts

• By examining the coefficient of the squared term in the quadratic function

How do you find the x-intercepts of a quadratic function?

• By finding the average of the x-values

• By taking the derivative of the function

• By adding the y-intercept to the slope of the function

• By setting the function equal to zero and solving for x using the quadratic formula or factoring.

What is the maximum or minimum value of a quadratic function and how is it related to the vertex?

• The maximum or minimum value is unrelated to the vertex

• The maximum or minimum value is the x-coordinate of the vertex

• The maximum or minimum value is always 0

• The maximum or minimum value is related to the vertex by being the y-coordinate of the vertex.

What is the significance of the y-intercept in the graph of a quadratic function?

• It represents the value of the function when x=1.

• It has no significance in the graph of a quadratic function.

• It indicates the maximum value of the function.

• It represents the value of the function when x=0.

How do you determine the domain and range of a quadratic function from its graph?

• You can determine the domain by counting the number of x-intercepts and the range by counting the number of y-intercepts on the graph.

• The domain can be found by looking at the vertex of the parabola and the range can be found by looking at the axis of symmetry on the graph.

• The domain is determined by the steepness of the parabola and the range is determined by the width of the parabola on the graph.

• You can determine the domain by looking at the x-values and the range by looking at the y-values on the graph.

What is the process of finding the equation of a quadratic function given its graph?

• Identifying key points on the graph and using them to form the equation

• Using trigonometric functions to calculate the equation

• Guessing the equation based on the graph's shape

• Counting the number of lines intersecting the graph

How do you use transformations to graph a quadratic function?

• Use a compass and straightedge to draw the graph

• Ask someone else to graph the function for you

• Apply translations, reflections, and stretches/shrinks to the parent function

• Use a protractor to measure the angles of the graph

What is the discriminant of a quadratic function and how is it used to determine the nature of the roots?

• It is used to determine the axis of symmetry of the quadratic function.

• It is used to determine the nature of the roots of the quadratic function.

• It is used to find the slope of the quadratic function.

• It is used to calculate the y-intercept of the quadratic function.