Quadratic Transformations Review

Front

What is a quadratic function?

Back

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

Front

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

Back

The 'a' value affects the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards. The larger the absolute value of 'a', the narrower the parabola.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a) in the standard form y = ax^2 + bx + c.

Front

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

Back

In the vertex form y = a(x - h)^2 + k, 'h' represents the x-coordinate of the vertex and indicates horizontal translation.

Front

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

Back

In the vertex form y = a(x - h)^2 + k, 'k' represents the y-coordinate of the vertex and indicates vertical translation.

Front

How does adding a constant outside the quadratic function affect the graph?

Back

Adding a constant outside the function, such as y = x^2 + c, translates the graph vertically. If c is positive, the graph moves up; if negative, it moves down.

Front

What is the effect of a horizontal translation on a quadratic function?

Back

A horizontal translation occurs when the x variable is adjusted, such as in y = (x - h)^2. This shifts the graph left (if h is positive) or right (if h is negative).

Front

What is a vertical stretch in a quadratic function?

Back

A vertical stretch occurs when the 'a' value is greater than 1 in the function y = ax^2. This makes the parabola narrower.

Front

What is a vertical compression in a quadratic function?

Back

A vertical compression occurs when the 'a' value is between 0 and 1 in the function y = ax^2. This makes the parabola wider.

Front

What does the transformation y = (x + 3)^2 represent?

Back

This transformation represents a horizontal shift of the graph of y = x^2 to the left by 3 units.