2.1 Quadratic Review

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

How do you find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value determines the direction of the parabola's opening: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, there are two real roots; if = 0, there is one real root; if < 0, there are no real roots.

Front

How can you find the vertex using completing the square?

Back

To find the vertex using completing the square, rewrite the quadratic in the form y = a(x - h)² + k, where (h, k) is the vertex.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, characterized by its U-shape.