Find the vertex of the parabola whose equation is y = x 2 + 8x + 12. (-4, 12) (-4, -4) (0, -6)

(-4, -4)

Step-by-step explanation:

You have to put this in vertex form by completing the square in order to determine the vertex.  Begin by setting the quadratic equal to 0 then moving the 12 over by subtraction:

The rules are to take half the linear term, square it, and add it to both sides.  Our linear term is 8.  Half of 8 is 4, and 4 squared is 16.  So we add 16 to both sides:

During this process we have created a perfect square biomial on the left. We will state that, along with simplifying on the right:

Now we will move the 4 back over and set it back to equal y:

And from this you can see that the coordinates of the vertex are (-4, -4)

A pair of jeans cost 40 dollars

A sweater costs 15 dollars

Step-by-step explanation:

Let s = cost a of sweater

j = cost of a pair of jeans

4s +2j = 140

2s +3j = 150

I will use elimination to solve.  Multiply the second equation by -2

-2(2s +3j )= 150*-2

-4s -6j = -300

Add this equation to the first equation

-4s -6j = -300

4s +2j = 140

    -4j = -160

Divide by -4

-4j/-4 = -160/-4

j = 40

A pair of jeans cost 40 dollars

Now we need to find the cost of the sweater

2s +3j = 150

2s +3(40) = 150

2s+120 = 150

Subtract 120 from each side

2s +120-120=150-120

2s = 30

Divide by 2

2s/2=30/2

s = 15

A sweater costs 15 dollars