Completing the Square and Quadratic Formula

Front

What is the process of completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x + p)² = q, making it easier to solve for x.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant tell us about the solutions of a quadratic equation?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: D > 0 means two distinct real solutions, D = 0 means one real solution, and D < 0 means two imaginary solutions.

Front

Solve by completing the square: x² + 10x + 14 = -7

Back

x = -3, -7

Front

If the discriminant is zero, how many real solutions are there?

Back

There is 1 real solution.

Front

Complete the square: x² + 6x + 20

Back

(x + 3)² + 11

Front

If the discriminant is negative, what can we say about the solutions?

Back

There are two imaginary solutions.

Front

Solve by completing the square: y² + 10y = -9

Back

y = -1, -9

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

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.