Math III EOC Review #4

Front

What is the radius of the circle with equation x² + (y+6)² = 196?

Back

The radius is 14.

Front

What is the end behavior of f(x) = -x²(x+4)(x-3)³?

Back

As x → -∞, f(x) → -∞. As x → ∞, f(x) → -∞.

Front

Write a system of equations for the number of $20 and $50 bills Caitlin has if T = # of $20 and F = # of $50.

Back

T + F = 49; 20T + 50F = 1430.

Front

Solve for x and y: 3x + 2y = 16; 7x + y = 19.

Back

(2, 5)

Front

What are vertical asymptotes in a rational function?

Back

Vertical asymptotes are lines x = a where the function approaches infinity or negative infinity.

Front

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

Back

The radius is the square root of the constant term in the equation (x-h)² + (y-k)² = r².

Front

What does the leading coefficient of a polynomial indicate about its end behavior?

Back

If the leading coefficient is positive, the ends of the graph rise; if negative, the ends fall.

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

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

Back

The discriminant determines the nature of the roots: positive (two real roots), zero (one real root), negative (no real roots).