Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

The 'a' value determines 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 of a parabola is the highest or lowest point on the graph, depending on whether it opens up or down.

Front

How do you find the vertex of a quadratic function in vertex form?

Back

In vertex form, f(x) = a(x - h)² + k, the vertex is (h, k).

Front

What is the effect of a vertical stretch on 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 transformation occurs when you add a constant to the function f(x)?

Back

Adding a constant 'k' to f(x) results in a vertical translation of the graph by 'k' units.

Front

What transformation occurs when you subtract a constant from the x variable in f(x)?

Back

Subtracting a constant 'h' from the x variable results in a horizontal translation of the graph to the right by 'h' units.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards if the 'a' value in the quadratic function is negative (a < 0).

Front

How can you determine the direction a parabola opens from its equation?

Back

You can determine the direction by looking at the 'a' value in the quadratic equation; if 'a' is positive, it opens up, and if 'a' is negative, it opens down.

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).