Intercepts, Symmetry, and Circle Standard Form (Vocabulary)

A set of vocabulary flashcards covering intercepts, symmetry, and the standard form of the circle, as discussed in the lecture notes.

Intercept

A point where a graph crosses an axis.

x-intercept

The intercept on the x-axis; the y-value is 0; points are of the form (x, 0).

y-intercept

The intercept on the y-axis; the x-value is 0; points are of the form (0, y).

zero/root

Value(s) of x that make f(x) = 0; the x-intercepts are the roots of the equation.

solve for x when y=0

Set y equal to zero and solve for x to find x-intercepts.

solve for y when x=0

Set x equal to zero and solve for y to find y-intercepts.

factoring

Expressing a polynomial as a product of its factors; used to find zeros via the zero-product property.

zero product property

If ab = 0, then a = 0 or b = 0; used to find roots after factoring.

plus/minus square root

When solving equations like x^2 = a, the solutions are x = ±√a.

undefined

No real solution (e.g., taking the square root of a negative number).

x-axis

The horizontal axis of the Cartesian plane; equation y = 0.

y-axis

The vertical axis of the Cartesian plane; equation x = 0.

first quadrant

The region where x > 0 and y > 0.

second quadrant

The region where x < 0 and y > 0.

symmetry with respect to the x-axis

If (x, y) lies on the graph, then (x, −y) also lies on the graph.

symmetry with respect to the y-axis

If (x, y) lies on the graph, then (−x, y) also lies on the graph.

symmetry with respect to the origin

If (x, y) lies on the graph, then (−x, −y) also lies on the graph.

DISMO

Graphing software mentioned as a tool to visualize functions and graphs.

standard form of a circle

Equation (x − h)^2 + (y − k)^2 = r^2, where (h, k) is the center and r is the radius.

center of a circle

The point (h, k) that is the center in the standard circle form.

radius of a circle

The distance from the center to any point on the circle; denoted r.

distance formula

Distance between (x1, y1) and (x2, y2) is sqrt((x2 − x1)^2 + (y2 − y1)^2).