Linear Functions and Quadratics

These flashcards cover key concepts related to linear functions and quadratic equations from the lecture notes.

What is the slope-intercept form of a linear equation?

y = mx + b, where m is the slope and b is the y-intercept.

What does the slope (m) of a horizontal line signify?

The slope m of a horizontal line is 0.

What equation represents a vertical line?

The equation of a vertical line is x = k where k is a constant.

In the equation Ax + By + C = 0, what do A, B, and C represent?

A, B, and C are constant numbers.

How can you determine the slope of the line given the equation 3x + 2y = 4?

Rearranging the equation to slope-intercept form reveals that the slope m is -3/2.

What is the average rate of change of the cellphone cost function as given?

The average rate of change of cost is increasing at a rate of 10 cents per minute.

How would you find the linear function for the cellphone cost?

Use the points (100, 35) and (200, 45) to derive the linear function.

If the value of computer equipment decreases from $18,500 to $11,500 over 2 years, what is the slope of the linear function V(t)?

The slope is -$3,500 per year.

What does the vertex of a quadratic function represent?

The vertex represents the highest or lowest point of the parabola.

What is the form of a quadratic function?

A quadratic function can be written as f(x) = ax^2 + bx + c.

What do the coefficients a, b, and c determine in a quadratic function?

They determine the shape and position of the parabola.

What is a vertex in relation to a quadratic function V(h,k)?

The vertex is the point (h,k) where the parabola changes direction.

In the context of the rocket launch, what does h(t) = 256t^2 - 96t + 256 signify?

It represents the height in feet of the rocket above the ground at time t in seconds.

At what time does the rocket reach maximum height according to the quadratic equation given?

The rocket reaches maximum height at t = 3 seconds.

What is the initial height (h(0)) of the rocket given the function h(t)?

The initial height of the rocket is 256 feet.

How is total cost modeled when producing items according to the given equation?

Total cost is modeled by the equation C(x) = 0.05x^2 + 15x + 2000.

What does a minimum total cost imply in production?

A minimum total cost implies the least expense to produce a given number of items.