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.

Front

What does the vertex of a quadratic function represent?

Back

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

Front

How does changing the value of 'a' in f(x) = a(x - h)² + k affect the graph?

Back

Changing 'a' affects the width and direction of the parabola. If |a| > 1, the parabola is narrower; if 0 < |a| < 1, it is wider. If a < 0, the parabola opens downwards.

Front

What does the 'h' in the vertex form f(x) = a(x - h)² + k represent?

Back

The 'h' value represents the horizontal shift of the graph. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What does the 'k' in the vertex form f(x) = a(x - h)² + k represent?

Back

The 'k' value represents the vertical shift of the graph. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the effect of a vertical stretch on a quadratic function?

Back

A vertical stretch occurs when the value of 'a' is greater than 1, making the parabola narrower and taller.

Front

What is the effect of a vertical shrink on a quadratic function?

Back

A vertical shrink occurs when the value of 'a' is between 0 and 1, making the parabola wider and shorter.

Front

How do you identify the direction a parabola opens?

Back

The direction a parabola opens is determined by the sign of 'a' in the quadratic function. If a > 0, it opens upwards; if a < 0, it opens downwards.

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, k) is the vertex.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.