Transforming Standard to Vertex Form

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

To convert from standard form (y = ax² + bx + c) to vertex form (y = a(x - h)² + k), you can complete the square.

Front

What is the vertex of the parabola represented by the equation y = 2(x - 3)² + 5?

Back

The vertex of the parabola is (3, 5).

Front

What does the 'a' value in the vertex form of a quadratic equation indicate?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic expression in the form of a perfect square trinomial, allowing for easier conversion to vertex form.

Front

Convert the equation y = x² - 4x + 1 to vertex form.

Back

y = (x - 2)² - 3.

Front

What is the significance of the vertex in a parabola?

Back

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

Front

How do you find the x-coordinate of the vertex from the standard form of a quadratic equation?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a) from the standard form y = ax² + bx + c.

Front

What is the result of distributing (x + 4)(x - 2)?

Back

The result is x² + 2x - 8.

Front

What is the vertex of the parabola represented by the equation y = -1(x + 2)² + 3?

Back

The vertex of the parabola is (-2, 3).