NC Math 3 Review: Circles, Transformations and Piecewise

Front

What is the standard form of a circle's equation?

Back

(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

How do you complete the square for the equation x² + y² + 6x - 12y + 20 = 0?

Back

Group x and y terms: (x² + 6x) + (y² - 12y) = -20. Complete the square: (x + 3)² + (y - 6)² = 25.

Front

What is the formula for the circumference of a circle?

Back

C = 2πr, where r is the radius.

Front

What does a reflection over the x-axis do to a function?

Back

It flips the graph of the function over the x-axis.

Front

What is the effect of a vertical shift of 'k' units on a function?

Back

It moves the graph up if k is positive and down if k is negative.

Front

How do you find the center and radius of a circle from its equation?

Back

Rewrite in standard form (x - h)² + (y - k)² = r² to identify (h, k) as the center and r as the radius.

Front

What transformation does 'Left 1 unit' indicate?

Back

The graph of the function shifts 1 unit to the left.

Front

What is the effect of a stretch factor of -2 on a function?

Back

It vertically stretches the graph by a factor of 2 and reflects it over the x-axis.

Front

How do you determine the radius from the equation of a circle?

Back

The radius is the square root of the constant on the right side of the equation in standard form.

Front

What does the term 'piecewise function' mean?

Back

A function defined by multiple sub-functions, each applying to a certain interval of the domain.