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SOLVING PROBLES WITH QUADRATIC EQUATIONS

HEIGHT AND DISTANCE WORD PROBLEMS

"If the question asks for the maximum height or the distance of the maximum height (Vertex). here is how you will solve it."

  1. Subsitude the numbers in to the quadratic formula in it's corresponding letter and evaluate to recieve your two x-intercepts

  2. add and divide your x-intercepts by 2 to recieve your axis of symmetry and substitude that back into the standred form equation to recieve your optimal value

  3. Your vertex is your answer, create a "Therefore" statment stating the maximum height of the "thing" and if asked, how long it will take to reach the height

  4. (If in case), somtimes a question will ask when will the "thing" land. to find that out you look back at your two x-intercepts. One is negative and the other positive so your positive intercept is the answer to this question as you cannot land on a negative number.

 A fireball is fired and follows a path modeled by y=-0.1x^2+1.6x+5.7, where x is the horizontal distance from the start, and y is the vertical height of the ball.

A straight forward question can somtimes come up asking what is the intial height or how high somthing starts and that can be found quickly from your "c" value of the standered form equation which is "5.7".

AREA WORD PROBLEMS

 

When dealing with area problems using "The Quadratic Formula" you will only have to deal with two different shapes. More likley you will face with Squares and the other being Right triangles

SQUARE

"The length of a rectangle is 6 inches more than its width. The area of the rectangle is 91 square inches. Find the dimensions of the rectangle."

  1. Create two "let's" statements for the expression of the length (w+6) and the expression of the width (w). 

  2. create your equation, it should be "(w)(w+6)=91

  3. Evaluate your equation using the "FOIL method" and once finshed, place "91" on the other side of the equal sign switching it's signs and becoming the value for "c".

  4. Substitude the numbers into it's corresponding variables in the quadratic formula and solve until you recieve your two x-intercepts

  5. Substitude and evaluate your two       x-intercepts into the brackets of "w" and "w+6" (Your previous dimensions) and those are your new dimensions

  6. Create a "Therefore" statement stating you new dimensions

 

(In case), if they give you the area of the previuos square instead of the new one, look closely at the hints and what the dimensions will be. An example could be if the dimensions are doubled. You multiply or "double" your old area by "two" to get the new area of your dimensions. You will need to do this to find your "c" value and get the correct dimensions of the new square.

TRIANGLE

  1. When dealing with triangles, you will have to refer back to Grade 9 and use the formula "pythagoream therom" (a^2+b^2=c^2) subsitude the three expressions of the triangle into the pythagoream therom. Create a let's statment as well determining the sides of the expressions

  2. Expand and simplify/use the "FOIL method"

  3. move everything on one side and solve for "zero" by using the quadratic formula

  4. When you recieve your x-intercepts, you will only need the positive             x-intercept

  5. Substitude the positive x-intercept into all exressions of the right triangle and solve to recieve your new dimensions of the right triangle

  6. Create a "Therefore" statment for your new dimensions 

 

Usually a question such as this will be staright forward with no extra questions being asked.

 

CONSECUTIVE NUMBERS

  1. ​Simplify your problem, what are they asking? create two let's statments for the two equations that you make from the word problem. Since it asks "The product of two consecutive even numbers that equal to 63. You should have two equations. One should be "(x)" and the other being "(x+2)" as they are even numbers and will be multiplied to get "63". So your equation is (x)(x+2)=63.

  2. Once you have your equation, you will solve for your x-intercepts which will equal to your two new numbers. Place the number 63 on the other side of the equation and solve for "0". Use the quadratic formula to find your two integers.

  3. To finalize your answer. Write a "therefore" statment to recieve full marks on a question such as this, show all of your work as well!

"The product of two consecutive even numbers is 63, what are the numbers ?"

REVENUE PROBLEMS

 

  1. Understand the problem. Problems in quadratics that deal with revenue will be converted in to factored form as the increase of caculator prices will be in one bracket and a decrease of students wanting to buy more will be in another. so from what we can take from this problem, we can create the equation (20+5x)(300-30x) the first bracket being completely revolved around money and the other being the number of caculators being sold. First create a "Let's" statement for your variable "r" and "x" before solving this equation. (one variable "r" will be for your revenue and your other variable "x" can be for the number of caulators sold.

  2. The easiest way to solve this is by solving for both of the "x's" from each of the brackets indivually.

  3. You will recieve two answers for "x", add and divide both of the "x's" to recieve your a.o.s and sustitude that back into the equation and evaluate to recieve your maximum revenue which answers part "b" of your problem (your "r" value from you "Let's" statement has been solved), and the final answer that you evaluated from the expression (20+5x) will be your selling price (part "a" has been solved) to produce your maximum price as the question asked relates to money so that expression will give your answer. (Your "x" value from your "let's" statement has been solved)

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