Transformations of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically 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 of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens. It can be found using the formula (-b/2a, f(-b/2a)).

Front

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

Back

In the vertex form f(x) = a(x - h)² + k, the 'h' value represents the x-coordinate of the vertex and indicates a horizontal shift.

Front

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

Back

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

Front

How does a vertical stretch affect a quadratic function?

Back

A vertical stretch occurs when the 'a' value is greater than 1, making the parabola narrower and increasing the distance between points on the graph and the x-axis.

Front

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

Back

A vertical compression occurs when the 'a' value is between 0 and 1, making the parabola wider and decreasing the distance between points on the graph and the x-axis.

Front

What does a negative 'a' value indicate in a quadratic function?

Back

A negative 'a' value indicates that the parabola opens downward, meaning the vertex is the highest point on the graph.

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 = -b/(2a).

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, f(0)).