Module 4 Review

Front

What determines if a quadratic function opens upward or downward?

Back

The sign of the coefficient 'a' in the quadratic term ax^2. If 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Front

Are the terms solution, root, x-intercept, and zero interchangeable in the context of quadratic equations?

Back

True, they all refer to the values of x where the quadratic function equals zero.

Front

What is the first step in solving a quadratic equation by completing the square?

Back

Move the constant term to the other side of the equation.

Front

What does the expression -3i(4 + 2i) simplify to?

Back

6 - 12i.

Front

How do you complete the square for the expression x^2 + 12x + ____?

Back

Add 36 to complete the square, resulting in x^2 + 12x + 36.

Front

What is the standard form of a quadratic function?

Back

y = ax^2 + bx + c.

Front

What is the vertex of a parabola given by the quadratic function y = ax^2 + bx + c?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the quadratic formula used to find the roots of a quadratic equation?

Back

x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant (b² - 4ac) tell us about the roots of a quadratic equation?

Back

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

What is the axis of symmetry for a parabola represented by the equation y = ax^2 + bx + c?

Back

The axis of symmetry is the vertical line x = -b/(2a).