ALGEBRA 1-REPORTING CATEGORY 4

Front

What is a vertical shift in a graph?

Back

A vertical shift occurs when a graph moves up or down on the coordinate plane. For example, f(x) = x² - 1 represents a vertical shift down by 1 unit from the graph of f(x) = x².

Front

What does the domain of a function represent?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For example, a domain of all real numbers less than -4 means x can take any value less than -4.

Front

How do you identify the x-intercepts of a quadratic function in factored form?

Back

The x-intercepts of a quadratic function in factored form, such as h(x) = (x + 1)(x - 3), can be found by setting each factor equal to zero: x + 1 = 0 and x - 3 = 0, giving x = -1 and x = 3.

Front

What is a quadratic function?

Back

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

Front

What does the range of a function represent?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. For example, a range of all real numbers greater than or equal to 3 means y can take any value starting from 3 and going upwards.

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 whether it opens upwards or downwards. It can be found using the formula x = -b/(2a) for the vertex's x-coordinate.

Front

What is the significance of the leading coefficient in a quadratic function?

Back

The leading coefficient (the coefficient of x²) determines the direction of the parabola: if it is positive, the parabola opens upwards; if negative, it opens downwards.

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

If the leading coefficient is positive, the quadratic function has a minimum value at the vertex. If it is negative, the function has a maximum value at the vertex.

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is expressed as f(x) = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots or x-intercepts of the function.