Quadratic Functions review

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

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

Back

For a function in vertex form f(x) = a(x - h)² + k, the vertex is the point (h, k).

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 equation x = h for the vertex form.

Front

What is the range of a quadratic function in vertex form when a > 0?

Back

The range is [k, +∞) if the vertex is at (h, k).

Front

What is the range of a quadratic function in vertex form when a < 0?

Back

The range is (-∞, k] if the vertex is at (h, k).

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' in the vertex form f(x) = a(x - h)² + k is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

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

How can you convert from standard form to vertex form?

Back

You can convert by completing the square on the standard form equation.

Front

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

Back

The 'a' value determines the width and direction of the parabola; larger |a| values make the parabola narrower.

Front

What is the formula for finding the x-coordinate of the vertex in standard form?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a).