Question

Which equation is a quadratic equation?

y = −4(3x + 2)

y + 3x3 = (x − 2)(3x + 8)

y − 3 = (2x2 + 11)(x − 1) + 3x

y + 5x = −2x(4 − x) + 1

Answer 1

Think about this: which equation would result in quadratic term(s) as the highest degree?

Answer 2

Hint: Distribute everything out for each equation and look for the one with the highest degree of 2.

Answer 3

Is it the second one...? I just do not understand.

Answer 4

Ok, let's go through each one:

#1: \[y = −4(3x + 2)\]Once you distribute, you end up with:
\[y=-12x-8\]In this equation, the highest degree is 1 (because of the -12x term which is the same as -12x^1).

#2: \[y + 3x^3 = (x − 2)(3x + 8)\]Once you distribute, you end up with:
\[y + 3x^3 = 3x^2-6x+8x-16\]In this equation, the highest degree is 3 (because of the 3x^3 term).

#3: \[y − 3 = (2x^2 + 11)(x − 1) + 3x\]Once you distribute, you end up with:
\[y − 3 = 2x^3+11x-2x^2-11\]In this equation, the highest degree is 3 (because of the 2x^3 term).

#4: \[y + 5x = −2x(4 − x) + 1 \]Once you distribute, you end up with:
\[y + 5x = -8x+2x^2+1\]In this equation, the highest degree is 2 (because of the -8x^2 term)....so this one is quadratic.

Answer 5

I see a small typo, there should be a +3x at the end of my distributed version of #3. Either way, that doesn't matter as the equation isn't quadratic.

Answer 6

I understand this so much clearer now, thank you! I still have a few i'm struggling on but I'll attempt them.

Answer 7

Good attitude...the only way to learn this stuff is through practice :)

Answer 8

Hopefully this didn't confused you but that last sentence (for #4) should have read:

"In this equation, the highest degree is 2 (because of the 2x^2 term)....so this one is quadratic."

I should proof-read more before clicking the button!