Converting Standard to Vertex Form (Completing the Square)

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 expression to vertex form?

Back

To convert a quadratic expression 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, making it easier to analyze and graph.

Front

What is the first step in completing the square for the expression x² + bx?

Back

The first step is to take half of the coefficient of x (which is b), square it, and add it to both sides of the equation.

Front

If you have the expression x² + 8x, what value do you add to complete the square?

Back

You add (8/2)² = 16 to complete the square.

Front

What is the vertex of the parabola represented by the equation y = (x + 4)² - 17?

Back

The vertex of the parabola is (-4, -17).

Front

How do you find the value of 'c' that completes the square in the expression t² + 7t + c?

Back

To find 'c', calculate (7/2)² = 49/4.

Front

What is the vertex form of the quadratic equation y = 2x² - 12x + 22?

Back

The vertex form is y = 2(x - 3)² + 4.

Front

What does the 'a' in the vertex form y = a(x - h)² + k represent?

Back

The 'a' represents the vertical stretch or compression of the parabola and its direction (upward if a > 0, downward if a < 0).

Front

How do you determine the direction of a parabola from its vertex form?

Back

The direction of the parabola is determined by the sign of 'a': if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.