Question 1:
For this case we must indicate the graph corresponding to:
[tex]y = x ^ 2+6x+9[/tex]
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:
[tex]3+3 = 6\\3 * 3 = 9[/tex]
So:[tex]y = (x+3) (x+3) = (x+3) ^ 2[/tex]
We use the form of vertex of a parabola:
[tex]y = a (x-h) ^ 2+k\\y = (x+3) ^ 2[/tex]
So:
a = 1
h = -3, is moved 3 units to the left
k = 0
The vertex of the parabola is given by: [tex](h, k) = (- 3,0)[/tex]
Since [tex]a = 1> 0[/tex]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:
[tex]A = a * b[/tex]
Where a and b are the sides of the rectangle.
We have as data that:
[tex]a = 4x + 5\\b = 2x + 3[/tex]
Then, the area is given by:
[tex]A = (4x + 5) (2x + 3)[/tex]
We must apply distributive property, which by definition establishes that:
[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]
Then the area of the rectangle is given by:
[tex]A = 8x ^ 2 + 12x + 10x + 15\\A = 8x ^ 2 + 22x + 15[/tex]
Answer:
Option D
