absolute value functions, Algebra 1 Questions help

I have listed the following questions below. I have received the explanations and answers to the questions. I don’t understand them and I would like you to help me understand the concepts better and know how to solve these types of questions. Thank you.

Solve by completing the square.
-2y2 + 8y = .98
Write your answers as integers, proper or improper fractions in simplest form, or decimals
rounded to the nearest hundredth.
or y =
You answered:
y =
or y =
With quadratic equations (ax2 + bx + c = 0), you can solve by completing the square.
Step 1: Make sure that the left side of the equation looks like x2 + bx.
Step 2: Add
to both sides.
Step 3: Factor the left side as x +
Step 4: Take the square root and solve.
Step 1: Make sure that the left side of the equation looks like x2 + bx.
To make the left side of the equation look like x2 + bx, divide both sides by-2.
-2y2 + 8y = -98
y2 – 4y = 49
Step 2: Add
b 2
to both sides.
2
Since b = -4,
() = (-2)2 = 4. Add 4 to both sides.
=
2
y2 – 4y + 4 = 53
52
Step 3: Factor the left side as x +
2
In general, an expression of the form x2 + bx
b 2
can be factored as
s(x+g)?.
The expression y2 – 4y + 4 is of this form, with b = -4. So, it can be factored as (y – 2)2.
Rewrite the equation with the left side factored.
(y-2)2 = 53
Step 4: Take the square root and solve.
y-2+7.28
Take the sque
e root
Y 2 = 7.28
Add 2 to both sides
y2 + 7.28 or y a 2 – 7.28
Split into + or –
y 9.28 or ye -5.28
Simplify
How does h(x) = 4.5* change over the interval from x = -4 to x = -3?
h(x) increases by 5
h(x) increases by a factor of 5
h(x) decreases by a factor of 5
h(x) increases by 500%
You answered:
To see how a function changes over an interval, look at the endpoints.
The values of h(x) = 4 . 5* at the endpoints x = -4 and x = -3 are:
h(-4) = 4.54
(-3) = 4.53
In the values 4.54 and 4.5-9, the same base is raised to different exponents. So, to see
how h(x) changes from x = -4 to x = -3, you should find the ratio of these two values.
-3
4.5
h(-3)
h(-4)
=
4.5-4
-3
=
53-4
Divide by subtracting the exponents
= 5
=
5h(-4). So, h(x) increases by a factor of 5 over the interval from x = -4
This means h(-3)
to x = -3.
out of 100
How does g(x)
1
change over the interval from x = 4 to x = 7?
7*
52
g(x) decreases by a factor of 73
g(x) increases by a factor of 21
g(x) decreases by a factor of 74
g(x) decreases by a factor of 21
You answered:
To see how a function changes over an interval, look at the endpoints.
The values of g(x)
at the endpoints x = 4 and x = 7 are:
g(4)
=
1
74
74
1
g(7) =
77
In the values and 27, the same base is raised to different exponents. So, to see how g(x)
changes from x = 4 to x = 7, you should find the ratio of these two values.
g(7)
9(4)
=
1
77
1
74
74
77
II
= 74 – 7
Divide by subtracting the exponents
= 73
=
1
73
This means g(7) = 949). So, g(x) decreases by a factor of 7 over the interval from x = 4 to
x = 7.
How does g(x)
=
1
change over the interval from x = 4 to x = 7?
7*
g(x) decreases by a factor of 73
g(x) increases by a factor of 21
g(x) decreases by a factor of 74
g(x) decreases by a factor of 21
You answered:
To see how a function changes over an interval, look at the endpoints.
The values of g(x) = at the endpoints x = 4 and x = 7 are:
7*
1
g(4)
=
1
g(7) = 77
In the values and ;;, the same base is raised to different exponents. So, to see how g(x)
changes from x = 4 to x = 7, you should find the ratio of these two values.
9(7)
g(4)
1
77
1
74
74
77
= 74-7
Divide by subtracting the exponents
= 73
1
73
This means 9(7) = 94.9). So, g(x) decreases by a factor of 7′ over the interval from x = 4 to
x = 7.
Graph this function:
y = 1x – 3| + 1
Click to plot the vertex first.
108
8
6
4
2
– 10
– 8
-6
-4
-2
0
N
4
6
8
10
-2
-4
-6
-8
– 10
You answered:
10Y
8
6
4
2
-10
– 8
-6
-4
-2
0
2
4
6
8
10
-2
-4
-6
-8
-10
The graph of the function y = |x-al + b is shaped like a V. The vertex is at the point (a, b).
The slope to the right of the vertex is 1, and the slope to the left of the vertex is – 1.