Algebra 2 Fall 24-25 Final Review #1

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: D > 0 means two real solutions, D = 0 means one real solution, and D < 0 means two non-real solutions.

Front

How do you factor the expression 3a² + 4a + 1?

Back

The expression factors to (3a + 1)(a + 1).

Front

What is the range of the function f(x) = -|x + 1| + 4?

Back

The range is (-∞, 4].

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the axis of symmetry for the quadratic function f(x) = ax² + bx + c?

Back

The axis of symmetry is given by the formula x = -b/(2a).

Front

What is the effect of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

Front

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

Back

Set f(x) = 0 and solve the equation ax² + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

What is the vertex of the parabola given by f(x) = -|x + 1| + 4?

Back

The vertex is at the point (-1, 4).

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value).