Unit 4 - Algebra 2 Quadratic Function Review

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the highest or lowest point of the parabola, depending on the direction it opens.

Front

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

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = h.

Front

What is the discriminant and how is it calculated?

Back

The discriminant is calculated using the formula D = b^2 - 4ac from the quadratic equation ax^2 + bx + c = 0. It determines the nature of the roots.

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a zero discriminant indicate about the roots of a quadratic equation?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.

Front

How do you shift a quadratic function vertically?

Back

To shift a quadratic function vertically, you add or subtract a constant from the function. For example, f(x) + k shifts it up by k units, while f(x) - k shifts it down by k units.

Front

How do you shift a quadratic function horizontally?

Back

To shift a quadratic function horizontally, you replace x with (x - h) for a right shift or (x + h) for a left shift, where h is the number of units to shift.