3.5 [IM2] 11.08.24

Front

What is the vertex of a quadratic function in the form f(x) = ax^2 + bx + c?

Back

The vertex can be found using the formula: (h, k) where h = -b/(2a) and k = f(h).

Front

How do you determine the vertex of the parabola given in vertex form y = a(x - h)^2 + k?

Back

The vertex is (h, k).

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax^2 + bx + c.

Front

What does the term 'compounded monthly' mean in finance?

Back

It means that interest is calculated and added to the principal balance every month.

Front

How do you calculate the future value of an investment with compound interest?

Back

Use the formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years the money is invested.

Front

What is the difference between exponential growth and decay?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over time, while exponential decay occurs when a quantity decreases by a fixed percentage over time.

Front

What is the formula for the future value of an investment compounded monthly?

Back

A = P(1 + r/12)^(12t), where A is the future value, P is the principal, r is the annual interest rate, and t is the time in years.

Front

How can you identify if a function is exponential growth or decay from its equation?

Back

If the base of the exponent is greater than 1, it is growth; if the base is between 0 and 1, it is decay.

Front

What is the significance of the coefficients a, b, and c in the quadratic equation f(x) = ax^2 + bx + c?

Back

The coefficient a determines the direction and width of the parabola, b affects the position of the vertex, and c is the y-intercept.

Front

What is the formula to find the y-coordinate of the vertex of a quadratic function?

Back

The y-coordinate of the vertex can be found using k = f(h), where h = -b/(2a).