Fall 2024 Semester Exam Part 3

Front

Identify the point (x_1,y_1) from the equation in point-slope form: y - 2 = -3(x + 5)

Back

The point is (-5, 2). This is derived from the point-slope form where (x_1, y_1) is the point (h, k) in the equation y - k = m(x - h).

Front

Multiply the polynomials: (3x² + 2x - 1)(x - 3)

Back

The result is 3x³ - 9x² - 7x + 3. This is found by distributing each term in the first polynomial by each term in the second polynomial.

Front

Simplify the radical \sqrt[]{200}.

Back

The simplified form is 10 \sqrt[]{2}. This is done by factoring 200 into 100 and 2, and taking the square root of 100.

Front

Which graph represents f(x) = |x| + 3?

Back

Graph C represents the function f(x) = |x| + 3, which is a V-shaped graph shifted up by 3 units.

Front

Simplify the expression: (3x² - 2x + 7) - (-5x² + 4x + 3).

Back

The simplified expression is 8x² + 6x + 4. This is done by distributing the negative sign and combining like terms.

Front

What is the definition of a polynomial?

Back

A polynomial is an algebraic expression that consists of variables raised to non-negative integer powers and coefficients.

Front

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

Back

The point-slope form is given by y - y_1 = m(x - x_1), where m is the slope and (x_1, y_1) is a point on the line.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex of a quadratic function in standard form y = ax² + bx + c can be found using the formula x = -b/(2a) for the x-coordinate.

Front

What is the difference between a rational and an irrational number?

Back

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a simple fraction.

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 ax² + bx + c = 0.