Many real life applications are modeled by quadratic functions. Think about some of the application problems in this lesson. What real life applications did you model using a quadratic function? It is important that you can name some of these applications. In particular, know that a revenue equation = xp where x is the number of goods sold and p is the price.
Other important objectives from 3.1 are.....
1. Write quadratic equations in quadratic form, or in vertex form, when given the graph with vertex and y-intercept.
2. Graph quadratic functions by hand by determining and labeling the vertex, axis of symmetry, y-intercept, vertical compression/stretch.
3. Given an equation in quadratic form, know the equation of the axis of symmetry, and know at first glance the y-intercept.
4. Know how the value of a determines if there is a vertical stretch, or a vertical compression.
5. EXTRA EXTRA EXTRA!! (required info that is not in our text)
The focus of the parabola (in vertex form) is k + 1/(4a) OR K - 1/(4a)
The LATUS RECTUM = 1/a (THE L.R. IS the line passing thru the focus.)
Please leave a comment if you have questions re. problems in this lesson.
Mrs. S
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5 comments:
I am pretty sure that I understand the overall lesson. However, I do not understand minimizing magrinal cost problems or analyzing the motion of a projectile problems.
Hi Tiffany,
Any time you are told to maximize profit, or minimize marginal cost, you are using x = -b/2a and y = f(-b/2a). (At this point, these marginal cost functions will be quadratic) I just posted a comment where I worked prob. 66 on page 191. It dealt with maximizing revenue. Study that comment after you finish the problem below.
Let's look at prob. 67 on page 191 The title tells us to minimize the marginal cost and we are given a cost equation which is quadratic. Notice in the problem that x = no. of tv's produced and C equals the marginal cost in dollars. (C is really y or f(x)). Notice the definition of marginal cost at the beginning of the problem. "If the marginal cost of producing the 50th product is $6.20, then it costs $6.20 to increase production from 49 to 50 units of output.
The problem asks "How many TV's should be produced to minimize the marginal cost?" Since x = the number of tv's produced, this question is asking you to find the minimum x value which is the x coordinate of the vertex of the parabola. How do we find the x coordinate of the vertex???? See if you can find it..you know the formula :)
The second question asks "What is the minimum marginal cost?" This question is asking you to find the lowest y value on the graph. Remember C is y for this equation. YOu just found the x coord. of the vertex. Now, plug in x and solve for C and you have the minimum marginal cost. Let me know if you have any more questions..
Tiffany's 2nd question was about projectile motion problems.
These problems are also quadratic.
Think about the path of a baseball...As the ball is hit, it goes up to a maximum height, then it comes down. The motion is in the shape of a parabola which is a quadratic function. Look at problem 77 page 192. The equation is quadratic and x is the horizontal distance.
a) This question wants you to find the x coordinate of the maximum point (the vertex) What does x equal for the vertex of a parabola?
b) The max. height is found by subbing your x answer for question a into the quadratic function and solving for h(x). (you are finding the max. y value)
c) To find this answer, you first need to sketch the situation.
We will finish showing this solution tomorrow in class. We need to be able to visualize the situation in order to fully understand it.
I agree with tiffany that the bulk of the lesson isn't too bad, but those problems like 67,73,77, and 78 are troubling me. I just don't understand. No matter how much I study the book I just can't seem to get it.
We'll look at those four first thing tomorrow.
Good night :)
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