Standard to Vertex Form

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = 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, complete the square on the quadratic expression.

Front

What is completing the square?

Back

Completing the square is a method used to convert a quadratic expression into a perfect square trinomial plus a constant.

Front

What is the vertex of the parabola represented by the equation y = (x - 5)² - 29?

Back

The vertex of the parabola is (5, -29).

Front

What does the 'a' value in the vertex form indicate about the parabola?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and its width (larger |a| means narrower, smaller |a| means wider).

Front

How do you find the axis of symmetry from the vertex form?

Back

The axis of symmetry can be found using the formula x = h, where (h, k) is the vertex.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

Convert the quadratic expression x² - 10x - 4 to vertex form.

Back

(x - 5)² - 29.

Front

Convert the quadratic expression x² - 12x + 38 to vertex form.

Back

(x - 6)² + 2.