Math 3 EOC Review

Front

What is the range of the function y = -3cos(2x) + 8?

Back

The maximum value is 8 + 3 = 11 and the minimum value is 8 - 3 = 5. The range is [5, 11].

Front

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

Back

For the equation x² + y² - 8x + 10y - 8 = 0, rewrite it in standard form. The center is (h, k) where h = 4 and k = -5.

Front

What is the inverse of the function y = (2x + 4)/8?

Back

The inverse is found by swapping x and y and solving for y. The inverse is y = (8x - 4)/2.

Front

How do you solve for x in an equation?

Back

Isolate x on one side of the equation using algebraic operations. For example, if the equation is 2x + 3 = 9, subtract 3 from both sides and then divide by 2.

Front

What are the zeros of a function?

Back

Zeros of a function are the x-values where the function equals zero. For the function with the graph, the zeros are -3 (multiplicity 2), 0, and 1.

Front

What is the amplitude of the function y = -3cos(2x) + 8?

Back

The amplitude is the absolute value of the coefficient of the cosine function, which is | -3 | = 3.

Front

How do you determine the period of a trigonometric function?

Back

The period of y = a sin(bx) or y = a cos(bx) is given by the formula 2π/|b|. For y = -3cos(2x), the period is 2π/2 = π.

Front

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

Back

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

Front

How do you find the vertex of a quadratic function?

Back

For a quadratic in standard form y = ax² + bx + c, the vertex can be found using the formula x = -b/(2a).

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.