Algebra 2 Midterm Review

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different parts of its domain.

Front

How do you determine the roots of a polynomial function?

Back

To find the roots of a polynomial function, set the function equal to zero and solve for the variable using factoring, the quadratic formula, or synthetic division.

Front

What is the quadratic formula?

Back

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

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph, meaning it can be drawn without lifting the pencil.

Front

What is the difference between real and complex roots?

Back

Real roots are solutions that can be plotted on the number line, while complex roots include imaginary numbers and cannot be represented on the number line.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, express the quadratic in the form (x - p)(x - q) = 0, then set each factor 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 distinct real roots; if zero, one real root; if negative, two complex roots.

Front

What is a root of a function?

Back

A root of a function is a value of x for which the function equals zero.

Front

How do you solve the equation x² = 5x - 10?

Back

Rearrange to x² - 5x + 10 = 0, then use the quadratic formula to find the roots.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q to easily solve for x.