*AA C&C Unit 4 Test REVIEW Part 1

Front

What is the general form of a polynomial equation with given zeros?

Back

If a polynomial has zeros at x = a, x = b, and x = c, the polynomial can be expressed as p(x) = k(x - a)(x - b)(x - c), where k is a constant.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the leading term of the polynomial. If the leading coefficient is positive and the degree is even, the ends of the graph rise. If the leading coefficient is negative and the degree is even, the ends fall. If the degree is odd, the ends will go in opposite directions.

Front

What is the discriminant in a quadratic equation, and what does it indicate?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It indicates the nature of the roots: if positive, there are two distinct real solutions; if zero, there is one real solution; if negative, there are two complex solutions.

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

How do you apply the Quadratic Formula to solve a quadratic equation?

Back

To apply the Quadratic Formula, identify the coefficients a, b, and c from the equation ax² + bx + c = 0, substitute them into the formula, and simplify to find the values of x.

Front

What is a polynomial's degree, and how does it affect the graph?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. It affects the number of turning points and the end behavior of the graph.

Front

What are the characteristics of a polynomial function's graph?

Back

Polynomial functions are continuous and smooth, can have multiple turning points, and their end behavior is determined by the leading term.

Front

What does it mean for a polynomial to have real solutions?

Back

Real solutions are the x-values where the polynomial intersects the x-axis. They can be found by factoring, using the Quadratic Formula, or graphing.

Front

How can you find the zeros of a polynomial function?

Back

Zeros of a polynomial function can be found by factoring the polynomial, using the Rational Root Theorem, or applying the Quadratic Formula for quadratic polynomials.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the direction of the graph's end behavior and influences the shape of the graph.