Quadratic Transformations

Front

What is a quadratic function?

Back

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

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the highest or lowest point on the graph, depending on the direction of the parabola.

Front

How does the value of 'a' in the quadratic function y = ax² affect the graph?

Back

The value of 'a' determines the direction and width of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. Larger absolute values of 'a' make the parabola narrower.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c.

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.

Front

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

Back

To find the vertex from the standard form y = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

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, where h is the x-coordinate of the vertex.

Front

What transformations occur when a quadratic function is written in vertex form?

Back

Transformations include vertical shifts (k), horizontal shifts (h), vertical stretches or compressions (a), and reflections over the x-axis.

Front

What does it mean to reflect a quadratic function over the x-axis?

Back

Reflecting a quadratic function over the x-axis means multiplying the function by -1, which flips the graph upside down.

Front

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

Back

A quadratic function opens upwards if 'a' is positive and downwards if 'a' is negative.