Completing the square practice

Front

What is the process of completing the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, where p and q are constants. This method allows for easier solving of the equation.

Front

How do you complete the square for the equation x² + 6x - 4 = 36?

Back

To complete the square, first move -4 to the right side: x² + 6x = 40. Then, take half of 6 (which is 3), square it (9), and add it to both sides: (x + 3)² = 49. Finally, take the square root and solve for x.

Front

What are the roots of the equation x² + 6x - 4 = 36 after completing the square?

Back

The roots are x = 4 and x = -10.

Front

What is the first step in completing the square for the equation x² + 12x = 5?

Back

The first step is to move 5 to the right side: x² + 12x - 5 = 0.

Front

What number must be added to both sides to complete the square for x² + 12x = 5?

Back

You need to add 36 to both sides, since (12/2)² = 36.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you find the vertex of a parabola represented by a quadratic equation?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))) where f(x) is the quadratic function.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

What is the solution to the equation (x - 3)² = 49?

Back

The solutions are x = 10 and x = -4.

Front

What is the relationship between the coefficients of a quadratic equation and its roots?

Back

The sum of the roots is -b/a and the product of the roots is c/a, according to Vieta's formulas.