Precalculus Chapter 2 Review

Front

What is the vertex form of a parabola?

Back

The vertex form of a parabola is given by the equation: f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the y-intercept of a quadratic function?

Back

To find the y-intercept of a quadratic function f(x) = ax² + bx + c, set x = 0 and solve for f(0) = c.

Front

What is the significance of the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero. They represent the x-intercepts of the graph.

Front

How do you determine the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have at most n zeros, counting multiplicities.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is given by: f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How do you convert from standard form to vertex form for a quadratic?

Back

To convert from standard form f(x) = ax² + bx + c to vertex form, complete the square.

Front

What is the axis of symmetry for a parabola?

Back

The axis of symmetry for a parabola in vertex form f(x) = a(x-h)² + k is the vertical line x = h.

Front

What is the formula for finding the vertex of a parabola given in standard form?

Back

For a quadratic in standard form f(x) = ax² + bx + c, the vertex can be found using the formula: h = -b/(2a), k = f(h).

Front

What is the relationship between complex zeros and polynomial functions?

Back

Complex zeros of polynomial functions occur in conjugate pairs. If a + bi is a zero, then a - bi is also a zero.