Complete 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 allows for easier solving and graphing.

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 and a ≠ 0.

Front

How do you simplify √800?

Back

√800 = √(16 * 50) = √16 * √50 = 4√50 = 4√(25 * 2) = 4 * 5√2 = 20√2.

Front

When do you use the plus or minus symbol (±) in solving equations?

Back

The plus or minus symbol (±) is used after taking the square root of both sides of an equation, indicating that there are two possible solutions.

Front

What does the x-intercept of a function represent?

Back

The x-intercept of a function is the point where the graph intersects the x-axis, meaning the value of f(x) is zero.

Front

If f(x) = (x - 2)², what is the x-intercept?

Back

The x-intercept is at x = 2, since f(2) = (2 - 2)² = 0.

Front

What are the solutions for f(x) = (x + 3)² when f(x) = 4?

Back

The solutions are x = -1 and x = -5, since (x + 3)² = 4 leads to x + 3 = ±2.

Front

How do you solve n² = 18n + 40 by completing the square?

Back

Rearrange to n² - 18n - 40 = 0, then complete the square: (n - 9)² - 81 - 40 = 0, leading to (n - 9)² = 121, giving n = 20 or n = -2.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.