Depth Project: Depth Project Problem One: Finding Domain under a Radical
Part One:: Part One: Steps to follow Start with one polynomial Pull out the common Factor Set up your Box and Diamond Multiply your 1 st and 3 rd term and place it in the Top of the diamond, and your 2 nd term in the bottom. Find what multiplies to be the top and adds to be the bottom Complete the edges of the square Graph Write your domain
What it looks like on paper: What it looks like on paper
Part Two: Factoring : Part Two: Factoring For the Denominator of the equation. Using your Math skills find what factors create the equation Pull out the greatest common factor Graph Write your domain
On paper: On paper
Combine : Combine Your finial domain is based off of your X values that make your out put real numbers
Problem two Long Division Challenge: Problem two Long Division Challenge Given the following X intercepts solve using long division for the missing two. -1,-3,-4,-2, 3,7,4 Steps: Place above the line what multiplies by your dividing term Multiply your 2 nd variable by the number above the line Subtract the quantities Drop the next term
The 9th Power: The 9 th Power After your first division continue with a new x intercept.
The 8th power: The 8 th power Doing Great Keep Going!!
7th and 6th : 7 th and 6 th Your getting close but not done yet!
Last Three long divisions : Last Three long divisions
Now with all the long divisions your equation should look like: (x+1)(x+3)(x+4)(x+2)(x-3)(x-7)(x-4)(x^2-3x-40): Now with all the long divisions your equation should look like: (x+1)(x+3)(x+4)(x+2)(x-3)(x-7)(x-4)(x^2-3x-40) Use the guess and check method to solve for your final two solutions After you do your factoring finial equation should be: (x+1)(x+3)(x+4)(x+2)(x-3)(x-7)(x-4)(x-8)(x+5) Graph and find your domain as if it was under a radical [-5,-4] u [-3,-2] u [-1,3] u [4,7] u [8,oo]
Problem Three : Problem Three Farmer John’s Bird cage Farmer John is helping build a cage for two parrots at the local zoo. He has 120 feet of post and his length is twice as long as his height. He needs to fence everything but the floor level, what is his maximum surface area for the cage?
Slide 14: The three equations tell us: First Surface Area is equal to the area of each individual side added up Two all the poles add to 120 feet Three the length is twice as long as the height Create your equations using the information you are given
Solving for a variable: Solving for a variable Using substitution Using substitution placing your third equation into your newly found equation Use the circled equations substitute these into your first equation to solve for z
Slide 16: Use –b/2a to solve for your z variable Plug in your newly found variables into your 2 nd equation to solve for x Once you solve for the length of your posts you can solve for the surface area of the cage Use substation to help farmer john build his parrot cage!! Math Substitution
THAT’S MATH!!: THAT’S MATH!!