Transformation Quadratics

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.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the effect of a negative 'a' value in a quadratic function?

Back

A negative 'a' value reflects the parabola across the x-axis, making it open downwards.

Front

What does the term 'vertical stretch' mean in transformations?

Back

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

Front

What does 'vertical compression' mean in transformations?

Back

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

Front

How does the 'h' value in the vertex form of a quadratic function affect the graph?

Back

The 'h' value in the vertex form f(x) = a(x - h)² + k shifts the graph horizontally. If h is positive, the graph shifts to the right; if negative, it shifts to the left.

Front

What does the 'k' value in the vertex form of a quadratic function represent?

Back

The 'k' value in the vertex form f(x) = a(x - h)² + k shifts the graph vertically. If k is positive, the graph shifts up; if negative, it shifts down.

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

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.

Front

What transformation occurs when a quadratic function is written as f(x) = a(x - h)² + k?

Back

This form indicates a horizontal shift by 'h' and a vertical shift by 'k' from the parent function f(x) = x².