Front

What is the composition of functions?

Back

The composition of functions, denoted as (f ∘ g)(x), means applying function g to x and then applying function f to the result of g. For example, if f(x) = 1/x and g(x) = 3x + 2, then (f ∘ g)(2) = f(g(2)) = f(8) = 1/8.

Front

How do you find the vertex of a parabola given its equation?

Back

The vertex of a parabola in the form y = ax^2 + bx + c can be found using the formula x = -b/(2a). Substitute this x-value back into the equation to find the corresponding y-value.

Front

What is the focus of a parabola?

Back

The focus of a parabola is a point from which distances to points on the parabola are measured. For a parabola that opens horizontally, the focus is located at (h + p, k) where (h, k) is the vertex and p is the distance from the vertex to the focus.

Front

What is the directrix of a parabola?

Back

The directrix of a parabola is a line that is perpendicular to the axis of symmetry and is located at a distance p from the vertex, opposite to the focus. For a parabola that opens horizontally, the directrix is given by the equation x = h - p.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function f(x) at a specific point x = a, substitute a into the function. For example, if f(x) = x^2 - 3, then f(2) = 2^2 - 3 = 1.

Front

What is the center of an ellipse?

Back

The center of an ellipse is the midpoint between its two foci. For an ellipse in standard form, (x-h)^2/a^2 + (y-k)^2/b^2 = 1, the center is at the point (h, k).

Front

What are the lengths of a and b in the equation of an ellipse?

Back

In the standard form of an ellipse, (x-h)^2/a^2 + (y-k)^2/b^2 = 1, 'a' is the semi-major axis length and 'b' is the semi-minor axis length. The lengths are determined by the values of a and b in the equation.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function represents the maximum or minimum point of the parabola. It is the point where the function changes direction.

Front

How do you find the center of a circle given its equation?

Back

The center of a circle in standard form (x-h)^2 + (y-k)^2 = r^2 is given by the point (h, k).

Front

What is the relationship between the focus and directrix of a parabola?

Back

The focus and directrix of a parabola are used to define the parabola. Any point on the parabola is equidistant from the focus and the directrix.