Unit 7 Review

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. For example, the absolute value of -17 is 17, written as | -17 | = 17.

Front

What are coordinate points?

Back

Coordinate points are pairs of numbers that define a position in a two-dimensional space, represented as (x, y). The first number is the x-coordinate (horizontal position), and the second is the y-coordinate (vertical position).

Front

What is a vertex in 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 quadratic equation ax^2 + bx + c.

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax^2 + bx + c.

Front

How do you complete the square for the expression x^2 + 4x?

Back

To complete the square, take half of the coefficient of x (which is 4), square it (2^2 = 4), and add it to the expression: x^2 + 4x + 4 = (x + 2)^2.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean for a function to have a minimum value?

Back

A function has a minimum value at a point where the function's value is lower than at any nearby points. This is often found at the vertex of a parabola that opens upwards.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of a quadratic equation. If it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

How do you factor a trinomial like x^2 + 4x + 4?

Back

To factor the trinomial x^2 + 4x + 4, look for two numbers that multiply to 4 and add to 4. The factors are (x + 2)(x + 2) or (x + 2)^2.

Front

What is the vertex form of a quadratic function?

Back

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