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 'vertical stretch' mean in the context of quadratic functions?

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 the context of quadratic functions?

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

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

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.