Graphing Quadratics

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a) for the quadratic equation in the form y = ax^2 + bx + c.

Front

How do you find the vertex of the quadratic function y = -5x^2 - 20x - 26?

Back

The vertex is (-2, -6). Use the formula x = -b/(2a) where a = -5 and b = -20.

Front

What is the vertex of the function f(x) = 2(x - 5)^2 + 12?

Back

The vertex is (5, 12). This is in vertex form, where (h, k) = (5, 12).

Front

How do you determine the range of a quadratic function?

Back

The range of a quadratic function can be determined by identifying the vertex and the direction of the parabola. If it opens upwards, the range is [k, ∞) and if it opens downwards, the range is (-∞, k] where (h, k) is the vertex.

Front

What is the range of the function y = -2x^2 + 4x + 3?

Back

The range is y ≤ 5, since the vertex is (1, 5) and the parabola opens downwards.

Front

What does the term 'axis of symmetry' refer to 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 can you identify the direction of a parabola?

Back

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

Front

What is the standard form of a quadratic equation?

Back

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

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

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square.