Final Review

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by h(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts of a quadratic function, set h(x) = 0 and solve for x.

Front

What is the relationship between the arc length and the circumference of a circle?

Back

The arc length is a fraction of the circumference, calculated as (arc length / circumference) = (angle in degrees / 360).

Front

What is the formula for the circumference of a circle?

Back

The circumference C of a circle is given by C = πd, where d is the diameter.

Front

How do you determine the diameter of a circle from its equation?

Back

For a circle in the form (x-h)² + (y-k)² = r², the diameter is d = 2r.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

How do you express the nth term of a geometric sequence?

Back

The nth term w of a geometric sequence can be expressed as w = a * r^(n-1), where a is the first term and r is the common ratio.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points?

Back

The slope m of a line through points (x1, y1) and (x2, y2) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation ax² + bx + c = 0. If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.