Int 2B commonly missed questions on Final

Front

What are the side lengths of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the side lengths are in the ratio 1 : √3 : 2. If the shortest side (opposite the 30° angle) is x, then the lengths are x (30°), x√3 (60°), and 2x (hypotenuse).

Front

How do you factor the expression 2x² + 22x + 60?

Back

To factor 2x² + 22x + 60, first factor out the common factor of 2: 2(x² + 11x + 30). Then, factor the quadratic: 2(x + 5)(x + 6).

Front

What is the vertex of the quadratic function y = (x - 3)² + 5?

Back

The vertex of the function y = (x - 3)² + 5 is (3, 5). This is the point where the graph reaches its minimum value.

Front

How do you complete the square for the expression x² + 12x + ____?

Back

To complete the square for x² + 12x, take half of the coefficient of x (which is 12), square it (6² = 36), and add it: x² + 12x + 36.

Front

What transformation occurs in the graph of y = (x - 5)²?

Back

The graph of y = (x - 5)² shifts to the right by 5 units compared to the graph of y = x².

Front

What is the formula for the area of a triangle?

Back

The area of a triangle is given by the formula: Area = 1/2 * base * height.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².

Front

How do you find the roots of a quadratic equation?

Back

To find the roots of a quadratic equation ax² + bx + c = 0, use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value).

Front

What does it mean to factor an expression completely?

Back

Factoring an expression completely means breaking it down into its simplest form, where no further factoring is possible.