Algebra 2 Checkpoint 2 Review

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

Front

How do you solve an absolute value equation like |x| = a?

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the vertex of a quadratic function in standard form?

Back

For a quadratic in standard form y = ax² + bx + c, the vertex can be found using the formula h = -b/(2a) and then substituting h back into the equation to find k.

Front

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

Back

Reflecting a function across the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic expression in the form (x + p)² + q, which makes it easier to analyze and graph.

Front

What is the sum of the roots of a quadratic equation ax² + bx + c = 0?

Back

The sum of the roots can be found using the formula -b/a.

Front

What is the range of a quadratic function that opens downwards?

Back

The range of a downward-opening quadratic function is all values less than or equal to the y-coordinate of the vertex.

Front

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

Back

To find the x-intercepts, set the quadratic equation equal to zero and solve for x.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.