Standard Form to Vertex Form

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is written as 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.

Front

What is completing the square?

Back

Completing the square is a method used to convert a quadratic equation into vertex form by adding and subtracting the same value to create a perfect square trinomial.

Front

What is the vertex of the parabola represented by the equation f(x) = 2(x + 1)² + 8?

Back

The vertex of the parabola is (-1, 8).

Front

What does the 'a' value in 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 (narrower if |a| > 1, wider if |a| < 1).

Front

Convert the quadratic equation y = x² + 4x into vertex form.

Back

y = (x + 2)² - 4.

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

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

Back

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

Front

What is the y-coordinate of the vertex when given the x-coordinate?

Back

Substitute the x-coordinate back into the original equation to find the corresponding y-coordinate.