Quadratic Transformations 1

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 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 parabola?

Back

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

Front

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

Back

'h' represents the x-coordinate of the vertex, and 'k' represents the y-coordinate of the vertex.

Front

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

Back

A negative 'a' value reflects the parabola over the x-axis.

Front

How does the 'c' value in the standard form of a quadratic function affect the graph?

Back

The 'c' value represents the y-intercept of the graph, indicating where the parabola crosses the y-axis.

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

What does a vertical stretch by a factor of 'k' do to the graph of a quadratic function?

Back

A vertical stretch by a factor of 'k' (where k > 1) makes the parabola narrower, while a vertical compression (0 < k < 1) makes it wider.

Front

What is the effect of translating a quadratic function to the right by 'h' units?

Back

Translating a quadratic function to the right by 'h' units involves replacing x with (x - h) in the function.

Front

What does it mean to reflect a quadratic function over the x-axis?

Back

Reflecting a quadratic function over the x-axis means multiplying the entire function by -1, which flips the parabola upside down.