Complete the Square (Vertex Form)

Front

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

Back

Completing the square involves rewriting a quadratic expression in the form of (x - p)² + q, where (p, q) represents the vertex of the parabola.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the vertex of a parabola given in vertex form?

Back

The vertex can be directly identified as the point (h, k) from the vertex form f(x) = a(x - h)² + k.

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 the direction it opens (upward or downward).

Front

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

Back

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

Front

What is the first step in completing the square for the expression x² + bx?

Back

The first step is to take half of the coefficient b, square it, and add it to both sides of the equation.

Front

Given the quadratic expression x² + 6x + 5, what is the completed square form?

Back

The completed square form is (x + 3)² - 4.

Front

What does the 'a' value in the vertex form f(x) = a(x - h)² + k indicate?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and its width (larger |a| means narrower, smaller |a| means wider).

Front

How do you determine the y-intercept of a quadratic function in vertex form?

Back

To find the y-intercept, substitute x = 0 into the vertex form equation and solve for f(0).

Front

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

Back

The vertex lies midway between the roots of the quadratic equation, and the x-coordinate of the vertex can be found using x = -b/(2a) from the standard form.