Quadratic Function
WORD PROBLEMS IN VERTEX/FACTORED FORM
Usually appication problems in vertex/factored form are simple and straight forward questions as the equation itself provides everything or a fewthings you need to solve the questions that come up. In quadratics, here is what questions usually come up to solve for in vertex, factored, and standard form and how to answer them. (Standard form problems will be left out as you will learn it in the unit after factored form which you are going to learn next after vertex form. As well, factored form and vertex form are alike and have almost the same steps to solve these kinds of questions). In application problems for quadratics, to recieve full marks in each of the application questions they ask. Create a "Let's" statment, show your work, solve for the answers, and finally a "Therefore" statment concluding your resolved problem. These simple 4-steps will give you full marks when solving application problems.
PROJECTILE PROBLEMS
When a question comes up and asks the maximum height of the "thing" it is a straight forward question in vertex form but requires steps in factored form. Your "k" value is the answer for this question so in factored form, you add the two x- intercepts together and divide them by "two" to get your (a.o.s) and substitude that back into your factored form equation and solve again to recieve your optimal value or "k" value.
Your "h" value in vertex form will be your answer to when it reaches your maximum height. For factored form as explained in the last step above, Your (a.o.s) is your "h" value which also is the answer to when the "thing" reached it's maximum height.
Substitude any variables excepth for "y" "0" and solve for the "y" value.For factored form, substitude "x" with "zero" and solve to recieve your answer.
Substitude "t" with "2" and solve for "h" using bedmas and recieve your answer. For factored form, Substitude "x" with "2" and solve to recieve your answer.
PROFIT PROBLEMS (VERTEX FORM ONLY)
Profit questions are easier in vertex form to solve as in part a, you already have your "h" and "k" value. In factored form, it will require more steps to solve but questions like these only allow you to solve in vertex form.
Profit questions are a simple two part questions. One is for finding the selling price and maximum profit which you can simply find on your vertex equation. and the other is "what is the selling price if the profits are equalled to zero ?" that you can simply find by subsituding "P" with zero and using reverse bedmas to solve for "S".