3.7 - Practice - Converting 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, you can complete the square.

Front

What does the 'a' value in the vertex form indicate?

Back

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

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

If a quadratic function is given as y = 2(x-3)² + 4, what is the vertex?

Back

The vertex is (3, 4).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex, given by the equation x = h.

Front

How can 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 y = ax² + bx + c.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic in the form y = ax² + bx + c into the form y = a(x-h)² + k.

Front

Convert the quadratic equation y = x² + 6x + 8 to vertex form.

Back

y = (x + 3)² - 1.

Front

What is the effect of changing the 'h' value in the vertex form?

Back

Changing the 'h' value shifts the parabola left or right along the x-axis.