Please help i need this done in atleast 2 hrs

Question

Task 1

Nonlinear Systems of Equations

Create a system of equations that includes one linear equation and one quadratic equation.

Part 1. Show all work in solving your system of equations algebraically.

Part 2. Graph your system of equations and show the solution graphically to verify your solution.

Task 2

Polynomial Identities

Part 1. Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)² = x² − 2xy + y² to square your number without using a calculator.

Part 2. Choose two values, a and b, each between 8 and 15. Show how to use the identity a³ + b³ = (a + b)(a² − ab + b²) to calculate the sum of the cubes of your numbers without using a calculator.

Answer 1

Hi Yadiel.

I'm wondering if you're overwhelmed by ALL the POWER YOU have over this problem.

You have been given complete control over every part of the problem.

You can make the problem difficult or keep it easy.

Task 1

Let's start by completing part 2 FIRST.

Pick a simple quadratic equation that would be easy to graph.

How about y = x² - 4. (Yeah, trust me, you're gonna like this one.)

The y-intercept is (0, -4)

Plot that point, and then 3 points on either side of the y-axis. (7 altogether.)

(USE GRAPH PAPER. If you have to download some from the internet and print it.)

Pick two points on the parabola that line up with the grid lines and draw the line that connects them.

These will give us integer values for our x's and y's.

Determine the slope-intercept form of the equation of the line.

Set the parabola equal to the line.

x² - 4 = mx + b

(Your m and b will be numbers)

Solve this equation for x. You'll get 2 answers.

They better be the x-coordinates of the points YOU PICKED.

Substitute those values in for x and find the values for the y's.

Here again, you know what the answers HAVE to be.

Task 2

Part 1

Pick a number greater than 25. (OMG so much freedom!)

I'm going to pick a number smaller, just to demonstrate.

(I also want to make you do some of this work on your own.)

I'll pick 16.

Now I need to describe 16 as the difference between two other numbers.

Again, the possibilities are endless, but I'm going to pick numbers that will be easy to work with.

I pick 16 = 20 - 4.

my x is 20 and my y is 4

Now the problem wants us to demonstrate that;

16² = (20 - 4)² = 20² - 2(20)(4) + 4²

16² = 400 - 160 + 16 = 256

Your numbers will be different, but I think this explains what the teacher is looking for.

Part 2

Here again, I'm going to pick 2 numbers smaller than 8 just to demonstrate.

I'll use 6 for a and 7 for b.

Substitute these into the form and I get;

(6³ + 7³) = (6 + 7)(6² - 6(7) + 7²

(216 + 343) = (13)(36 - 42 +49)

559 = (13)(43)

559 = 559

Now pick some number on your own give it a try.

I hope this helps.