Cumulative 3

Front

What is the quadratic formula used to solve equations of the form ax^2 + bx + c = 0?

Back

Front

How do you simplify the expression (5i + 4) - (2i + 3)?

Back

Combine like terms: (5i - 2i) + (4 - 3) = 3i + 1.

Front

What is the maximum height of a projectile launched vertically with an initial velocity of 128 feet per second?

Back

The maximum height occurs at t = 4 seconds, calculated using the vertex formula for the quadratic equation.

Front

What is the product of two complex numbers (3 - 2i) and (7 + 6i)?

Back

The product is calculated as follows: (3)(7) + (3)(6i) + (-2i)(7) + (-2i)(6i) = 21 + 18i - 14i - 12 = 33 + 4i.

Front

What are the roots of the equation x^2 - 6x + 4 = 0?

Back

Front

What does it mean for a quadratic function to have a maximum or minimum value?

Back

A quadratic function has a maximum value if it opens downwards (a < 0) and a minimum value if it opens upwards (a > 0).

Front

How do you find the vertex of a parabola represented by the equation h(t) = -16t^2 + 128t?

Back

The vertex can be found using the formula t = -b/(2a). Here, t = 128/(2 * -16) = 4 seconds.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the standard form of a quadratic equation?

Back

Front

How do you multiply two complex numbers in the form a + bi and c + di?

Back

Use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2, where i^2 = -1.