Convert 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 in standard form to vertex form?

Back

To convert from standard form y = ax² + bx + c to vertex form, you can complete the square.

Front

What is the vertex of the parabola represented by the equation y = -x² + 10x - 4?

Back

The vertex of the parabola is (5, 21).

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.

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 can 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 process of completing the square?

Back

Completing the square involves rewriting a quadratic expression in the form of a perfect square trinomial, which helps in converting to vertex form.

Front

Convert the quadratic equation y = x² - 2x - 5 to vertex form.

Back

The vertex form is y = (x - 1)² - 6.

Front

What is the vertex of the function f(x) = 3x² + 6x - 5?

Back

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

Front

How do you determine the y-coordinate of the vertex after finding the x-coordinate?

Back

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