Fall Final Review (Honors Precalculus)

Front

What is the average rate of change of a function?

Back

The average rate of change of a function over an interval [a, b] is given by the formula: \( \frac{f(b) - f(a)}{b - a} \). It represents the slope of the secant line connecting the points (a, f(a)) and (b, f(b)).

Front

Calculate the average rate of change of the function \( f(x) = 2x^2 + 1 \) at the interval \( x = 0 \) and \( x = 1 \).

Back

The average rate of change is \( 2 \).

Front

What is the formula for the length of a side in a triangle given two sides and the included angle?

Back

The length of a side can be found using the Law of Cosines: \( c^2 = a^2 + b^2 - 2ab \cos(C) \).

Front

If \( f(x) = 2x^2 + 12x + 16 \), what is the average rate of change of \( f(x) \) on the interval [-1, x]?

Back

The average rate of change is \( 2x + 10 \).

Front

What is the equation of a sine function with an amplitude of 2?

Back

The equation is \( y = 2 \sin(x) \).

Front

What does the absolute value equation \( |5 - 2x| = 9 \) represent?

Back

It represents two equations: \( 5 - 2x = 9 \) and \( 5 - 2x = -9 \).

Front

Solve the equation \( |5 - 2x| = 9 \).

Back

The solutions are \( x = -2 \) or \( x = 7 \).

Front

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

Back

The vertex of a quadratic function \( f(x) = ax^2 + bx + c \) represents the maximum or minimum point of the graph, depending on the sign of \( a \).

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula \( x = -\frac{b}{2a} \) and then substituting back to find \( f(x) \).

Front

What is the general form of a quadratic function?

Back

The general form is \( f(x) = ax^2 + bx + c \), where \( a \neq 0 \).