Enhanced Algebra Georgia Milestones EOC Study Guide 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 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.

Front

What does the axis of symmetry represent in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a) for the function f(x) = ax^2 + bx + c.

Front

How do you find the vertex of a quadratic function in standard form?

Back

To find the vertex of a quadratic function in standard form f(x) = ax^2 + bx + c, use the formula (h, k) where h = -b/(2a) and k = f(h).

Front

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

Back

The discriminant, given by D = b^2 - 4ac, determines the nature of the roots of the quadratic equation ax^2 + bx + c = 0. 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

What is the factored form of the quadratic function f(x) = x^2 + 5x + 6?

Back

The factored form is f(x) = (x + 2)(x + 3).

Front

How do you convert a quadratic function from standard form to vertex form?

Back

To convert from standard form f(x) = ax^2 + bx + c to vertex form, complete the square.

Front

What is the range of a quadratic function that opens upwards?

Back

The range of a quadratic function that opens upwards is [k, ∞) where (h, k) is the vertex of the parabola.

Front

What is the range of a quadratic function that opens downwards?

Back

The range of a quadratic function that opens downwards is (-∞, k] where (h, k) is the vertex of the parabola.

Front

What does the mean represent in a data set?

Back

The mean is the average of a set of numbers, calculated by dividing the sum of all values by the number of values.