Completing The Square Practice

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 the equation y = (x + 7)² + 3?

Back

The vertex is (-7, 3). This is derived from the vertex form where h = -7 and k = 3.

Front

What is the process to complete the square for the expression x² + 8x + c?

Back

To complete the square, take half of the coefficient of x (which is 8), square it (4² = 16), and add it to c.

Front

What value of c completes the square for x² + 8x + c?

Back

The value of c that completes the square is 16.

Front

What are the roots of the equation v² + 2v - 23 = 0?

Back

The roots are {-1 + 2√6, -1 - 2√6}.

Front

How do you solve the equation n² - 4n + 71 = 4?

Back

First, rearrange it to n² - 4n + 67 = 0, then use the quadratic formula or complete the square to find the roots.

Front

What is the significance of the b value in completing the square?

Back

The b value is halved and squared to find the constant term needed to complete the square.

Front

What is the formula for the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant (b² - 4ac) tell you about the roots of a quadratic equation?

Back

The discriminant indicates the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

How can you convert a quadratic equation from standard form to vertex form?

Back

You can convert by completing the square on the standard form equation.