Completing the Square, Big Review

Front

What is 'Completing the Square'?

Back

Completing the Square is a method used to solve quadratic equations by rewriting them in the form (x + p)² = q, making it easier to find the roots.

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 complete the square for the equation x² + 8x + 16?

Back

To complete the square, rewrite it as (x + 4)², since 4 is half of 8 and 4² = 16.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, no real roots.

Front

Solve for x: x² - 16 = 0.

Back

x = ±4.

Front

What is the process of evaluating a quadratic expression?

Back

To evaluate a quadratic expression, substitute the value of x into the expression and simplify.

Front

Evaluate: x² + 4x + 4 when x = 2.

Back

The evaluation gives 12.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a, which divides the parabola into two mirror-image halves.

Front

How do you find the roots of a quadratic equation using completing the square?

Back

Rearrange the equation to isolate the constant, complete the square, and then solve for x.