Complete the Square and Convert from Standard to Vertex

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 find the vertex of a parabola given in vertex form?

Back

In vertex form y = a(x - h)² + k, the vertex is the point (h, k).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

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 does completing the square involve?

Back

Completing the square involves rewriting a quadratic equation in the form y = a(x - h)² + k by manipulating the equation.

Front

What is the significance of the 'a' value in the vertex form?

Back

The 'a' value determines the direction and width of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the vertex of the parabola given by y = 3(x + 5)² - 4?

Back

The vertex is (-5, -4).

Front

Which function is equivalent to y = x² - 6x + 10?

Back

y = (x - 3)² + 1.

Front

How do you determine the vertex from the equation y = x² - 2x - 5?

Back

Convert to vertex form: y = (x - 1)² - 6, so the vertex is (1, -6).

Front

What is the vertex of the parabola y = 5(x - 2)² - 7?

Back

The vertex is (2, -7).