Quadratic Transformations

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 does the 'a' value in a quadratic function affect?

Back

The 'a' value affects 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 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 does changing 'h' in the vertex form affect the graph?

Back

Changing 'h' shifts the graph left or right. If h is positive, the graph shifts right; if h is negative, it shifts left.

Front

How does changing 'k' in the vertex form affect the graph?

Back

Changing 'k' shifts the graph up or down. If k is positive, the graph shifts up; if k is negative, it shifts down.

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

What is the effect of compressing a quadratic function vertically?

Back

Compressing a quadratic function vertically makes the parabola wider. This occurs when the absolute value of 'a' is between 0 and 1.

Front

What is the effect of stretching a quadratic function vertically?

Back

Stretching a quadratic function vertically makes the parabola narrower. This occurs when the absolute value of 'a' is greater than 1.

Front

What does the term 'transformation' refer to in the context of quadratic functions?

Back

Transformation refers to changes made to the graph of a function, including shifts, reflections, stretches, and compressions.

Front

How do you determine the direction of a parabola from its equation?

Back

The direction of a parabola can be determined by the sign of 'a' in the quadratic equation. If a > 0, it opens upward; if a < 0, it opens downward.