T8 & 11 Quadratics & Statistics Review Flashcard

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula x = -b/(2a) for the function f(x) = ax^2 + bx + c.

Front

How do you find the zeros of a quadratic function?

Back

The zeros of a quadratic function can be found by solving the equation ax^2 + bx + c = 0 using factoring, completing the square, or the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing on an interval if the output values rise as the input values increase. It is decreasing if the output values fall as the input values increase.

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the coefficient 'a' in the quadratic function f(x) = ax^2 + bx + c. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

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

Back

The discriminant, given by D = b² - 4ac, determines the nature of the roots of the 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 convert a quadratic function to vertex form?

Back

To convert a quadratic function from standard form f(x) = ax^2 + bx + c to vertex form f(x) = a(x - h)² + k, complete the square.

Front

What is a survey in statistics?

Back

A survey is a method of collecting data by asking people questions to gather information about their preferences, opinions, or behaviors.

Front

How do you calculate the percentage of a group?

Back

To calculate the percentage of a group, divide the number of individuals in the subgroup by the total number of individuals in the group and multiply by 100.