Module 4 Review

Front

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

Back

Completing the square involves rearranging a quadratic equation into the form (x + p)^2 = q, allowing for easier solving by taking the square root of both sides.

Front

How do you take the square root of both sides of an equation?

Back

To take the square root of both sides of an equation, apply the square root operation to each side, remembering to include both the positive and negative roots.

Front

What does the plus or minus symbol (±) indicate in solutions?

Back

The plus or minus symbol indicates that there are two possible solutions: one where the value is added and one where it is subtracted.

Front

How do you simplify the expression -3i(4 + 2i)?

Back

To simplify -3i(4 + 2i), distribute -3i to both terms: -3i * 4 = -12i and -3i * 2i = 6. Thus, the simplified expression is 6 - 12i.

Front

What are the roots of the quadratic equation x^2 - 5x + 10 = 0?

Back

The roots are (5 - i√15)/2 and (5 + i√15)/2, which are complex numbers.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

What is the discriminant in a quadratic equation, and what does it indicate?

Back

The discriminant is given by b^2 - 4ac. It indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

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

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k is the value of the quadratic function at h.