Question

Solve the quadratic equation below and describe what the solution represents on a graph Show your work so i can understand

0 = x2 + 5x + 6

Answer 1

Megan, are you allowed to use a graphing calc on this problem?

Answer 2

no sadly not

Answer 3

i just need to know the points on the vertex

Answer 4

Ok. Well, you can factor this. :) Do you know how to factor a quadratic?

Answer 5

yes but i dont understand the factors of 5 and 6

Answer 6

Well you want to write the equation like this:

\[(x +a )(x +b)\]

Where a times b = 6 and
a plus b = 5

So the question is ... what two numbers make that true?

Answer 7

oh sorry 3 and 2 multiply to get 6 and add up to 5 i understand a lil better now

Answer 8

Yay! Ok, so we're almost there. :)

\[(x+3)(x+2) = x^2+5x+6\]

So when is \((x+3)(x+2)=0)\) ?

Hint it's wherever (x+3) = 0 or (x+2) = 0

Answer 9

x= -3? and x= -2?

Answer 10

Yup! So now we know that this quadratic equation intersects the x axis at x = -2 and x = -3. Since the \(x^2\) term is positive, that means the parabola opens upward. The vertex is at the x value EXACTLY between -2 and -3.

Answer 11

so is that the answer?

Answer 12

Well, you solved the qudratic. (found the values of x which made it true). As for the graph, can you now sketch the parbola knowing what we found out?

Answer 13

x^2 + 5x + 6=0
x^2+(3x+2x) +6=0
(x^2+3x)+(2x+6)=0
x(x+3)+2(x+3)=0
(x+3)(x+2)=0
either ,
(x+3)=0 or,
(x+2)=0

therefore, x =-3 or x =-2

Answer 14

yes i think so do i need y?

Answer 15

Well if you're going to sketch it, you need an x an y axis. :)

Answer 16

if i want to get the y dont i just take one of the x's and put it in the equation?

Answer 17

Yes.

So when x = - 3 or - 2, y will be zero.

What about when x = -2.5 ? What will y equal?

Answer 18

y=31?

Answer 19

This is cheating a bit, but it gives a clue.
http://www.wolframalpha.com/input/?i=y+%3D+x%5E2+%2B+5x+%2B+6+

Answer 20

when x = -2.5 , then y=0

Answer 21

oh so y just equals 0?

Answer 22

"when x = -2.5 , then y=0 "

This is incorrect.

y only equals 0 for x = -2 and x = -3. For all other values of x, y is nonzero.

Answer 23

To see what this graph looks like, go to

http://www.wolframalpha.com
and type in
x^2 + 5x + 6 for x = - 4 to -1

Answer 24

so on the graph i jus put (-2.5,0)

Answer 25

Unfortunately, when x= -2.5 (or -5/2) y does not equal 0
Try again!

Answer 26

so could i just but like (-2,0)?

Answer 27

I would plot (-2,0). (-3, 0) and the middle point at (-5/2 , ??) and sketch a U shaped curve.
Try to find y when x= -5/2.

Answer 28

1/2((-2,0)+(-3, 0))= ((-2-3)/2,(0+0)/2) =(-5/2,0)

Answer 29

@ab
we are trying to plot y=x^2 + 5x + 6.

Answer 30

ok i think i will plot it at (-2,0) and (-3,0)

Answer 31

y= (-5/2)^2 + 5(-5/2) +6
y= 25/4 - 25/2 +6
Can you finish?

Answer 32

Another easy point to find is when x=0
y= 0^2 +5*0 +6 =6
so (0,6) is also on the curve

Answer 33

ok thanks yah i can finishh