1.  Consider the parabola f(x) = 3(x-2)2– 1 andthe line g(x) = 9x -2.(i)  On graph paper sketch the line and the parabola.  Indicate clearly the vertex of the parabola, as well as x- or y-intercepts for either. Be sure to use exact (fractions and radicals) expressions.(ii)  Calculate exactly the two intersection points of the parabola and line, and label them on your sketch. Do this by completing the square.(iii)  Between the intersections, the line is above the curve.  Write an equation for h(x), the function giving the height of the line above the curve.  Simplify h(x) into ax2  + bx + c form for your final answer.(iv)  What is the DOMAIN of h(x)? Answer this one in a complete sentence.(v)  Ok, now complete the square to write your h(x) in the form A(x-_)2+B.(vi)  Use (v)to find the greatest distance between the line and curve.(vii)  Mark this distance with a BAR on your sketch, and label exactly, with coordinates, the top and bottom of the BAR.

1. Now consider the parent function P(x) = x2, and let g(x) = 4(x-1)2 + 8.(A) Explain step-by-step, graphing/labeling (on graph paper!) the parent, each intermediate function, if we do transformations in these two orders: (You will have to figure out the exact transformations in each case.)   (i)Horizontal shift then vertical stretch then vertical shift;  (ii)Horizontal shift then vertical shift then  vertical stretch.(B) (i) Explain how you can cut the domain of our g(x) so that at least part of it has an inverse function (I.e. passes the horizontal line test).  (ii) Now find the equation of the INVERSE function of our g(x).

Two-Variable Inequalities Read the following instructions to complete this assignment: Solve problem 68 on page 539 of Elementary and Intermediate Algebra, and make sure to study the given graph. For the purposes of the assignment, it would be helpful to copy the graph onto your own scratch paper.                                                                                                                                                Week 2 assignment 001.jpg                                                                                                                                   Write a two- to three-page paper (not including the title page) that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example  (attached) MAT222.W2.AssignmentExample.pdf , and be concise in your reasoning. In the body of your essay, do the following: Demonstrate your solution to all three portions of the above problem, making sure to include all mathematical work, and an explanation for each step.   Use the inequality you create from part (a) of problem 68 to evaluate the following two scenarios: The Burbank Buy More store is going to make an order which will include, at most, 60 refrigerators. What is the maximum number of TVs that could also be delivered on the same 18-wheeler? Be sure to show all your work and how you came to that conclusion. The next day, the Burbank Buy More decides they will have a television sale so they change their order to include at least 200 TVs. What is the maximum number of refrigerators that could also be delivered in the same truck? Be sure to show your work and how you came to that conclusion. Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.): Solid line Dashed line Parallel Linear inequality Test point