Quadratic Review

Front

What is a quadratic function?

Back

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

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 ≠ 0.

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

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

Back

In vertex form, f(x) = a(x-h)² + k, the vertex is (h, k).

Front

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

Back

The 'a' value indicates 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

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

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

Back

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

Front

What transformation occurs when a quadratic function is shifted up?

Back

When a quadratic function is shifted up, the value of 'c' in the standard form increases, resulting in a vertical translation.

Front

What transformation occurs when a quadratic function is compressed vertically?

Back

A vertical compression occurs when the 'a' value is between 0 and 1, making the parabola wider.

Front

What transformation occurs when a quadratic function is stretched vertically?

Back

A vertical stretch occurs when the 'a' value is greater than 1, making the parabola narrower.