Flashcard 4 - Quadratic functions

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you find the vertex of a parabola given in vertex form?

Back

To find the vertex of a parabola in vertex form f(x) = a(x - h)² + k, the vertex is simply (h, k).

Front

What does the 'a' value in the vertex form indicate?

Back

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

Front

What is the effect of adding a constant outside the squared term in vertex form?

Back

Adding a constant outside the squared term (k) translates the parabola vertically. If k is positive, the parabola moves up; if k is negative, it moves down.

Front

What is the effect of subtracting a value from x in vertex form?

Back

Subtracting a value from x (h) translates the parabola horizontally. If h is positive, the parabola moves left; if h is negative, it moves right.

Front

How do you determine the axis of symmetry for a parabola?

Back

The axis of symmetry for a parabola in vertex form f(x) = a(x - h)² + k is the vertical line x = h.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How can you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square.

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

What does it mean for a parabola to be 'stretched' or 'compressed'?

Back

A parabola is 'stretched' if |a| > 1 (narrower) and 'compressed' if |a| < 1 (wider).