A2.Fall Final 2024

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, i.e., i = √(-1). It is used to express complex numbers.

Front

How do you simplify the expression -6 - √(-49) using imaginary numbers?

Back

The expression simplifies to -6 - 7i, since √(-49) = 7i.

Front

What is the formula for finding the y-intercept of a quadratic function?

Back

To find the y-intercept of a quadratic function in the form y = ax^2 + bx + c, substitute x = 0. The y-intercept is the value of y when x = 0.

Front

What is the y-intercept of the parabola y = x^2 - x + 3?

Back

The y-intercept is 3, found by substituting x = 0 into the equation.

Front

What is the x-intercept form of a quadratic equation?

Back

The x-intercept form of a quadratic equation is y = a(x - p)(x - q), where p and q are the x-intercepts.

Front

How do you determine the type of function from its graph?

Back

To determine the type of function from its graph, observe the shape: linear functions form straight lines, quadratic functions form parabolas, absolute value functions have a V shape, and constant functions are horizontal lines.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation ax^2 + bx + c = 0 and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you apply the quadratic formula to solve -8v^2 - 9v - 1 = 0?

Back

Identify a = -8, b = -9, c = -1, then substitute into the quadratic formula to find v = -1 or v = -1/8.

Front

What is a parabola?

Back

A parabola is a symmetric curve formed by the graph of a quadratic function. It can open upwards or downwards depending on the sign of the leading coefficient.

Front

What does it mean for a function to be quadratic?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax^2 + bx + c, where a ≠ 0.