Question

MULTIPLE QUESTIONS NEED HELP FAST 4O POINTS!!!!!!!

1. Which graph represents the solution of y ≤ x2 + 2?

A. upward opening parabola formed with a dashed curve, vertex at 0 comma 2, and shading inside parabola
B. upward opening parabola formed with a dashed curve, vertex at 0 comma 2, and shading outside parabola
C. upward opening parabola formed with a solid curve, vertex at 0 comma 2, and shading inside parabola
D. upward opening parabola formed with a solid curve, vertex at 0 comma 2, and shading outside parabola

2. What is the range of the function f(x) = |x| + 3?

A. {f(x) ∈ ℝ | f(x) ≤ 3}
B. {f(x) ∈ ℝ | f(x) ≥ 3}
C. {f(x) ∈ ℝ | f(x) > 3}
D. {f(x) ∈ ℝ | f(x) < 3}

3. A two-variable inequality is shown in the graph.

Graph: upward opening parabola which is solid with vertex at 1 comma 2, travels through points negative 1 comma 6 and 3 comma 6, with shading inside the curve

Which point is not included in the solution set for the inequality?

A. (0, 6)
B. (1, 5)
C. (2, 4)
D. (3, 2)

4. What is the solution for x2 –18x < –77?

A. x < –11 or x > 7
B. x < –7 or x > 11
C. –11 < x < 7
D. 7 < x < 11

5. What is the solution to the inequality |2x – 3| > 5?

A. x < –1 or x > 4
B. x < 0 or x > 8
C. 0 < x < 8
D. –1 < x < 4

Answer 1

The description of the graph shows that it is an upward opening parabola formed with a solid curve, vertex at 0 comma 2, and shading outside parabola

What is the graph of a parabola equation?

The graph of a parabola equation has a curved U-shaped dimension and takes the form of a quadratic equation f(x) =ax² + b + c

Using the parabola standard equation:

4p(y-k) = (x-h)²

where;

• Vertex is at (h,k), and
• Focal length = |p|

y ≤ x² + 2 can be written in standard form as:
$\mathbf{4\times \dfrac{1}{4}(y-2) =(x-0)^2}$

Thus, the parabola properties can be computed as:

• (h,k) = (0,2)
• p = 1/4

The graph y ≤ x² + 2 can be see in the attached image below.

From the graph, the description shows that:

• It is an upward opening parabola formed with a solid curve, vertex at 0 comma 2, and shading outside parabola.

The range of the function f(x) = |x|+3 is the values of f(x) that are greater than or equal to 3.

i.e.

• Range:  {f(x) ∈ ℝ | f(x) ≥ 3}

Option B is correct.

3.

The point that is not included in the solution set for the inequality is (1,5)

4.

The factor of the quadratic equation x² - 18x < - 77 is:
= (x -7) (x - 11) < 0

The solution becomes:

= 7 < x < 11

5.

The solution to the inequality |2x - 3| > 5 is:

= |2x - 3| > 5

Applying absolute rule:

= 2x - 3 < -5 or 2x - 3 > 5

= x < -1 or x > 4

Option A is correct.

Learn more about the graph of a parabola equation here:

https://brainly.com/question/12896871

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