Advanced Algebra and Functions

Front

What is the formula for the surface area of a right rectangular prism?

Back

Surface Area = 2(lw + lh + wh), where l = length, w = width, h = height.

Front

Calculate the surface area of a right rectangular prism with length 4 cm, width 9 cm, and height 3 cm.

Back

Surface Area = 2(4*9 + 4*3 + 9*3) = 2(36 + 12 + 27) = 2(75) = 150 cm².

Front

What is the process to factor the expression 3x² + 6x - 24?

Back

Factor out the greatest common factor (3): 3(x² + 2x - 8). Then factor the quadratic: 3(x + 4)(x - 2).

Front

What is the end behavior of a polynomial function when the leading coefficient is positive and the degree is odd?

Back

The graph will rise to the right and fall to the left.

Front

What is the value of f(x + 2) if f(x) = x² + 3x + 1?

Back

f(x + 2) = (x + 2)² + 3(x + 2) + 1 = x² + 4x + 4 + 3x + 6 + 1 = x² + 7x + 11.

Front

What is exponential growth in the context of population dynamics?

Back

Exponential growth occurs when the growth rate of a population is proportional to its current size, leading to rapid increases.

Front

If a population doubles every 4 hours, what is the growth factor for each hour?

Back

The growth factor for each hour is the 4th root of 2, approximately 1.1892.

Front

What is the general form of a quadratic function?

Back

The general form is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.