Algebra 2 Final Exam Review

Front

What is the amplitude of a trigonometric function?

Back

The amplitude of a trigonometric function is the maximum distance from the midline of the wave to its peak or trough. It is half the distance between the maximum and minimum values of the function.

Front

How do you find the maximum value of a trigonometric function given its amplitude and minimum value?

Back

To find the maximum value, add the amplitude to the minimum value. For example, if the amplitude is 4 and the minimum value is 5, the maximum value is 5 + 4 = 9.

Front

What is the process for factoring a polynomial given one of its factors?

Back

To factor a polynomial given one of its factors, use polynomial long division or synthetic division to divide the polynomial by the given factor, then factor the resulting polynomial further if possible.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does it mean if a quadratic equation has complex solutions?

Back

Complex solutions occur when the discriminant (b² - 4ac) is less than zero, indicating that the parabola does not intersect the x-axis.

Front

What is the period of a cosine function?

Back

The period of a cosine function is the length of one complete cycle of the wave. For the function y = A cos(Bx), the period is given by 2π/B.

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, multiply the degree measure by π/180. For example, to convert 200° to radians, calculate 200 × π/180 = 10π/9.

Front

What is the relationship between the amplitude and the vertical shift of a trigonometric function?

Back

The amplitude determines the height of the peaks and the depth of the troughs, while the vertical shift moves the entire graph up or down without affecting the amplitude.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots of the quadratic equation: if positive, there are two real roots; if zero, one real root; if negative, two complex roots.

Front

How do you determine the maximum and minimum values of a trigonometric function?

Back

The maximum value is found by adding the amplitude to the vertical shift, and the minimum value is found by subtracting the amplitude from the vertical shift.