Characteristics of Quadratic Graphs

Front

What is the domain of a quadratic function in a real-world context, such as the height of a golf ball above the ground?

Back

The domain represents the set of possible input values (x-values) for the function. In this context, it is the range of horizontal distances the golf ball can travel, typically expressed as 0 ≤ x ≤ 230.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a) for a quadratic in the form ax^2 + bx + c.

Front

How do you determine the maximum height of a quadratic function given in the form h(t) = -16t² + 8t + 24?

Back

To find the maximum height, use the vertex formula t = -b/(2a) to find the time at which the maximum occurs, then substitute this value back into the function to find the maximum height.

Front

What does it mean for a parabola to open upwards or downwards?

Back

A parabola opens upwards if the coefficient of x² (a) is positive, indicating a minimum vertex. It opens downwards if a is negative, indicating a maximum vertex.

Front

What is a vertex in the context of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

Front

What is the significance of the green dashed line in a quadratic graph?

Back

The green dashed line represents the axis of symmetry, which indicates where the parabola is symmetrical.

Front

How can you identify whether a quadratic function has a maximum or minimum value?

Back

If the parabola opens upwards, it has a minimum value at the vertex. If it opens downwards, it has a maximum value at the vertex.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the role of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward or downward) and affects the width of the parabola.

Front

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

Back

To find the x-intercepts, set the quadratic function equal to zero and solve for x using factoring, completing the square, or the quadratic formula.