Alg 2: 5.1-5.2 Flashcard Retake

Front

What is a horizontal translation in the context of function transformations?

Back

A horizontal translation shifts the graph of a function left or right along the x-axis. For example, f(x) = (x - 3)² translates the graph of f(x) = x² three units to the right.

Front

What is a vertical translation in the context of function transformations?

Back

A vertical translation shifts the graph of a function up or down along the y-axis. For example, f(x) = x² + 3 translates the graph of f(x) = x² three units up.

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 its orientation. It is a key point in determining the shape and position of the parabola.

Front

What does it mean when a parabola has a maximum vertex?

Back

A maximum vertex indicates that the vertex is the highest point on the graph of the parabola, meaning the parabola opens downwards.

Front

What does it mean when a parabola has a minimum vertex?

Back

A minimum vertex indicates that the vertex is the lowest point on the graph of the parabola, meaning the parabola opens upwards.

Front

How do you find the vertex of a parabola given in vertex form?

Back

In vertex form, y = a(x - h)² + k, the vertex is the point (h, k). For example, in y = 3(x + 5)² - 4, the vertex is (-5, -4).

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It passes through the vertex.

Front

How do you determine the direction a parabola opens?

Back

The direction a parabola opens is determined by the coefficient 'a' in the vertex form. If 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.