Semester Exam Study Guide Review 2024 Alg II

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be written in the form (a + b)² = a² + 2ab + b². For example, x² + 8x + 16 is a perfect square trinomial.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (3x - 1)(x + 5) = 3x² + 15x - x - 5 = 3x² + 14x - 5.

Front

What does the y-intercept of a line represent?

Back

The y-intercept of a line is the point where the line crosses the y-axis. It is represented by the value of y when x = 0.

Front

How do you write an absolute value function with transformations?

Back

To write an absolute value function with transformations, use the form y = a|x - h| + k, where (h, k) is the vertex, 'a' indicates reflection and vertical stretch/compression.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions are the values that satisfy all equations in the system.

Front

What is the formula for finding the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form y = ax² + bx + c can be found using the formula x = -b/(2a).

Front

What is the significance of the coefficient of x in a linear equation?

Back

The coefficient of x in a linear equation represents the slope of the line, indicating how much y changes for a unit change in x.

Front

How do you determine if a quadratic equation has real solutions?

Back

To determine if a quadratic equation ax² + bx + c = 0 has real solutions, calculate the discriminant D = b² - 4ac. If D > 0, there are two real solutions; if D = 0, one real solution; if D < 0, no real solutions.

Front

What is the relationship between the roots and the coefficients of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

Front

What does it mean for a function to be reflected across the x-axis?

Back

A function is reflected across the x-axis when its output values are multiplied by -1, resulting in the transformation y = -f(x).