Question

Task 2—Non-Linear Systems of Equations

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

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

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

Answer 1

@dan815 @ganeshie8 @iambatman

Answer 2

Make it very easy, just use something you can think of in your head.

Easiest quadratic equation, x^2. Easiest linear equation, x. They're also easy to graph and to find their solution, set x^2 = x. Divide each side by x, x = 1. When doing systems of linear and nonlinear equations, just think what the easiest example to satisfy the problem is!

Answer 3

Basically a parabola and a line.

Answer 4

I needed an f(x) = equation, and a y = mx + b forms

Answer 5

Just do what solomon said

Answer 6

? I don't know how to make a parabola

Answer 7

Make anything up! Any line and any parabola (opening up or down)

Answer 8

f(x) = x^2

Answer 9

y = x

Answer 10

Here, I"ll pick 2 that I know work.

f(x) = 2x + 1
y = x^2 + x - 2

Answer 11

I would try to have b=2,4, or other EVEN number.

Answer 12

I mean in ax^2+bx+c=0

Answer 13

I thank you all! Thank you so much, but can you explain your system @adam.bloedel

Answer 14

Please

Answer 15

I would choose

y=2x+2
f(x)=x²+4x+6

Answer 16

Yeah those are good :)

Answer 17

Well, by explain, I meant prove it was verified

Answer 18

I would listen to these guys. They know more about how equations act than I do. They can give in-depth nearly professional answers. I know @SolomonZelman and Batman are great at what they do. Listen to Solomon step you through it.

Answer 19

Will do, thank you!

Answer 20

Okay.

`y=x+2` (actually 1x, not 2x) would be just a line. It is same as y=x but shifted 2 units up and easy to work with.

And `f(x)=x²+4x+6`

Answer 21

`f(x) = x²+4x+6` → `f(x) = x²+4x+4+2` → `f(x) = (x+2)²+2`

Answer 22

They are verified as to be a proper system?
f(x) = (x+2)²+2 and y = x + 2

Answer 23

And there are you parabola f(x)=(x+2)²+2 and a line y=x+2

Answer 24

You can check that algebraically.

Answer 25

After this question, can I ask you guys something?

Answer 26

Do you know how to graph the equations?

Answer 27

Yes

Answer 28

I did

Answer 29

I changed y=x+2 to y=x+6 if you don't mind.

Answer 30

https://www.desmos.com/calculator/mt7rqitrms

Answer 31

How can I show you?
Well, it looks like this:
The parabola's minimum is -2,has no x-intercept, and y = 6

Answer 32

Oh, we changed it, ok

Answer 33

I have to draw it again lol, thanks for patience

Answer 34

Yes, I drew it, https://www.desmos.com/calculator/mt7rqitrms :)

Answer 35

They intercept!

Answer 36

The line:
x = (-6, 0)
y = (0, 6)
y = 1x + 6
Slope = 1
6 = y

Answer 37

So this is verified I believe

Answer 38

After this question, can I ask you guys something?

Answer 39

It has to do with my math course, you two seem to be extremely smart about math...