M. Alg II HW ck 5-1 A (NB 4-1)

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the definition of a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, which can be expressed in the standard form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How can you determine if a function is linear or quadratic?

Back

You can determine if a function is linear or quadratic by examining its highest degree term. If the highest degree is 1, it is linear; if it is 2, it is quadratic.

Front

What is the linear term in a quadratic equation?

Back

The linear term in a quadratic equation is the term that contains the variable raised to the first power, typically represented as bx in the standard form ax² + bx + c.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a).

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It is found at the coordinates (h, k) in the vertex form of a quadratic function.

Front

What is the standard form of a quadratic equation?

Back

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

Front

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

Back

The discriminant, given by the formula D = b² - 4ac, determines the nature of the roots of a quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How do you find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.