Question

Part 1:
Solve each of the quadratic equations below and describe what the solution(s) represent to the graph of each. Show your work to receive full credit.

y = x2 + 3x + 2
y = x2 + 2x + 1

Part 2:
Using complete sentences, answer the following questions about the two quadratic equations above.

Do the two quadratic equations have anything in common? If so, what?
What makes y = x2 + 3x + 2 different from y = x2 + 2x + 1?

Answer 1

i guess i should ask, have you learned factoring yet?

Answer 2

Yes, but I am realllyy bad at it :/

Answer 3

ok that easiest way to solve these quadratic equations
lets look at 1st one:
\[x^{2} + 3x + 2 = 0\]
we want to factor it so it looks like this
\[(x+a)(x+b) = 0\]
so
\[a*b = 2\]
\[a+b = 3\]
what 2 numbers will work?

Answer 4

Hmm..6?

Answer 5

what is 6?

2 numbers that multiply to 2 and add to get 3

Answer 6

Ohhh, 1 and 2?

Answer 7

yep
(x+1)(x+2) = 0

x = -1 and x = -2

Answer 8

lets do the 2nd one
\[x^{2} +2x+1 = 0\]
2 numbers that multiply to 1 and add to get 2

Answer 9

Why did you make them -1 and -2?

Answer 10

oh sorry, the 2 numbers we came up with 1 and 2 are used to factor the equation.
but we still have to solve for "x"

--> (x+1)(x+2) = 0
anything times 0 is 0 right
so you can take each factor and set it equal to zero to find "x"

--> x+1 = 0 --> x = -1

--> x+2 = 0 --> x = -2

these are the x-intercepts on the graph

Answer 11

Oh ok, and for the second one would it be 1 and 1?

Answer 12

yes

(x+1)(x+1) = 0

Answer 13

Okay

Answer 14

here are the graphs