Algebra 2 Finals SEM 1 Review 2024

Front

What is the end behavior of a polynomial function when it approaches negative infinity and positive infinity?

Back

For a polynomial function, the end behavior is determined by the leading term. If the leading coefficient is negative and the degree is odd, as x approaches -∞, y approaches ∞ and as x approaches ∞, y approaches -∞.

Front

Evaluate f(8) for the function f(x) = -3x^2 - 2x + 5.

Back

f(8) = -3(8)^2 - 2(8) + 5 = -192 - 16 + 5 = -203.

Front

Identify the x-intercepts of the function f(x) = 2(x-3)(x+4).

Back

The x-intercepts are found by setting f(x) = 0. Thus, x-3 = 0 or x+4 = 0, giving x = 3 and x = -4.

Front

What is the sum of the complex numbers 3 - 2i and 8 + 3i?

Back

The sum is (3 + 8) + (-2i + 3i) = 11 + i.

Front

How do you determine the number of relative maxima in a function's graph?

Back

Relative maxima can be identified by locating the peaks in the graph where the function changes from increasing to decreasing.

Front

What is the leading term of the polynomial g(x) = -5x^3 + 12x^2 - 7x + 11?

Back

The leading term is -5x^3, which determines the end behavior of the function.

Front

Define the term 'vertex' in the context of a quadratic function.

Back

The vertex of a quadratic function is the point where the graph changes direction, representing the maximum or minimum value of the function.

Front

What is the formula for finding the vertex of a quadratic function in standard form y = ax^2 + bx + c?

Back

The vertex can be found using the formula x = -b/(2a).

Front

Explain the significance of the y-intercept in a function's graph.

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).