Convert from 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, complete the square on the quadratic expression.

Front

What is the vertex of the parabola represented by the equation y = (x - 1)² - 6?

Back

The vertex is (1, -6).

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

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

Back

y = (x - 1)² - 6.

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 f(x) = x² + 12x - 2 into vertex form.

Back

f(x) = (x + 6)² - 38.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic expression in the form (x - p)² - q, where p and q are constants.

Front

Convert f(x) = 3x² + 6x - 5 to vertex form.

Back

f(x) = 3(x + 1)² - 8.

Front

What is the vertex of the parabola represented by f(x) = 4(x - 4)² - 62?

Back

The vertex is (4, -62).