Completing the Square

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 is done by adding and subtracting the square of half the coefficient of x.

Front

How do you complete the square for the expression x² + 6x?

Back

To complete the square, take half of the coefficient of x (which is 6), square it (3² = 9), and rewrite the expression as x² + 6x + 9.

Front

What is the completed square form of the quadratic equation x² + 14x?

Back

The completed square form is (x + 7)² - 49, since half of 14 is 7, and 7² = 49.

Front

What is the vertex form of a parabola?

Back

The vertex form of a parabola 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 parabola given by the equation y = 3(x + 5)² - 4?

Back

The vertex is found directly from the vertex form: (h, k) = (-5, -4).

Front

What is the significance of the vertex in a parabola?

Back

The vertex represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

What is the standard form of a quadratic equation?

Back

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

Front

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

Back

To convert, complete the square on the quadratic expression and rewrite it in the form y = a(x - h)² + k.

Front

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

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients from the standard form ax² + bx + c.

Front

What is the formula for the axis of symmetry of a parabola?

Back

The axis of symmetry is given by the line x = -b/(2a), which passes through the vertex.