Question

Someone please help me

Answer 1

Question 1:

For this case we must indicate the graph corresponding to:

$y = x ^ 2+6x+9$

We factor the expression by looking for two numbers that multiplied give as a result 9 and added as a result 6. These numbers are 3 and 3:

$3+3 = 6\\3 * 3 = 9$

So:$y = (x+3) (x+3) = (x+3) ^ 2$

We use the form of vertex of a parabola:

$y = a (x-h) ^ 2+k\\y = (x+3) ^ 2$

So:

a = 1

h = -3, is moved 3 units to the left

k = 0

The vertex of the parabola is given by: $(h, k) = (- 3,0)$

Since $a = 1> 0$then the parabola is concave upwards.

With these data we can conclude that the correct option is the option H.

Answer:

Option H

Question 2:

For this case we have by definition, that the area of a rectangle is given by:

$A = a * b$

Where a and b are the sides of the rectangle.

We have as data that:

$a = 4x + 5\\b = 2x + 3$

Then, the area is given by:

$A = (4x + 5) (2x + 3)$

We must apply distributive property, which by definition establishes that:

$(a + b) (c + d) = ac + ad + bc + bd$

Then the area of the rectangle is given by:

$A = 8x ^ 2 + 12x + 10x + 15\\A = 8x ^ 2 + 22x + 15$

Answer:

Option D

Answer 2

the graph for the given equation is (H), because

if you put x=-3,-1 and -5

Then value for y becomes 0, 4 and 4 respectively

i.e. (x,y)= (-3,0)(-1,4)(-5,4) which will satisfy the graph