Math 3 wk 2

Front

What is the quadratic formula?

Back

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

Front

How do you determine the number of solutions for a quadratic equation?

Back

The number of solutions can be determined using the discriminant (D = b² - 4ac). If D > 0, there are two distinct solutions; if D = 0, there is one solution; if D < 0, there are no real solutions.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers and coefficients. Example: 2x² + 3x - 5.

Front

How do you find the roots of a quadratic equation?

Back

Roots can be found using factoring, completing the square, or applying the quadratic formula.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What does it mean for a polynomial to be factored?

Back

Factoring a polynomial means expressing it as a product of its factors, which can be simpler polynomials. Example: x² - 5x + 6 = (x - 2)(x - 3).

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. Example: In 4x³ + 2x² - x + 7, the degree is 3.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): (a + b)(c + d) = ac + ad + bc + bd.

Front

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

Back

The leading coefficient is the coefficient of the term with the highest degree. It determines the end behavior of the polynomial's graph.