Complete the Square (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 find the vertex from the vertex form?

Back

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

Front

What does completing the square mean in the context of quadratic equations?

Back

Completing the square involves rewriting a quadratic equation in the form y = a(x - h)² + k to easily identify the vertex and graph the parabola.

Front

Given the equation y = 3(x + 5)² - 4, what is the vertex?

Back

The vertex is (-5, -4).

Front

Convert the quadratic equation y = x² + 10x + 23 to vertex form.

Back

The vertex form is y = (x + 5)² - 2.

Front

What is the process to complete the square for the equation f(x) = x² + 6x + 12?

Back

1. Take half of the coefficient of x (which is 6), square it (9), and add/subtract it: f(x) = (x² + 6x + 9) + 12 - 9 = (x + 3)² + 3.

Front

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

Back

The vertex is (3, 4).

Front

How do you convert the expression x² + 4x + 10 into completed square form?

Back

The completed square form is (x + 2)² + 6.

Front

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

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 axis of symmetry for a parabola in vertex form?

Back

The axis of symmetry is the vertical line x = h, where (h, k) is the vertex.