Determining the number of x-intercepts and the location of the vertex.

Without drawing the graph of the given equation, determine: (a) how many x-intercepts the parabola has (b) whether its vertex lies above or below the x-axis. y = -x^2 + 2x - 1

Finding the roots of an equation.

Solve. Leave answers in simplest radical form. x^2 + 8x = -16

Finding the roots of an equation.

Solve. Leave answers in simplest radical form. 3x^2 = 2x + 5

Calculating a mathematical model and extrapolating it to find other information.

The distance an object falls is directly proportional to the square of the time it has been falling. After 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 feet?

Change in variables with direct and inverse proportions.

x varies directly as the square of s and inversely as t. How does x change when s is doubled? When both s and t are doubled?

Solve an equation with degree higher than 2?

How would you go about trying to solve an equation with degree higher than 2? Would the number of terms in the equation dictate your method?

Finding the roots of an equation.

Solve: x^2 - x - 1 = 0

Solve the quadratic equation.

2x(to the second power)- 3x + 1 = 0

Polynomial functions: P(x)=5

I need to know how to solve p(x)=5 where p(x) is any polynomial.

Polynomials and real zeros

How can you prove that a 5th degree polynomial must have at least one real solution zero?