1.) A function is given

Question

h(x) ==
FX 2
How can be h(15) evaluated?
1
4 by multiplying 5 by the square of 15
by multiplying the square of 5 by the square of 15
1
@) by multiplying - by the square of 15, then dividing by 15
1
by multiplying the square of 5 by the square of 15,
then dividing by 15

2.) A function is shown.
y+ 1=2(x+3)
Which graph represents the function?
y
y
inMN- OHNMTI
5-
4.
13-
3
-2
-2
1-
=5-4-3/2-10
12345
x
x
-5-4-3-2-19/1 2 34 5
1,
3.
-5
-5
y
Y
5+
4.
4+ 1
34
3+
24
24/
1.
1.
x
x
-5-4-3-2-10
1234 5
-5-4-3-2-10 12345
2
12.
4.
5-

3.)The graph of a quadratic function is shown.
y
6++
4+
NO
2+
12 / 4/6
×
-6
1-2
-2+
Which equation represents the function?
A) y = - 2(x + 3)2 + 4
y = - (x - 3)2 + 4
0
y = (x + 3)2 + 4
D
= 6(x + 3)2 - 4

4.)A ball was dropped from a balcony at a height of 20 feet above level
ground. The height, in feet, of the ball after t seconds is modeled by the
function shown.
y = - 16t + 20
What is the range of the function in terms of the situation described?
@Ost
® Osy
00St≤ 20
0 ≤ y ≤ 20

Answer 1

Let's go through each question step by step.

Question 1: Evaluating the Function

The function provided seems to be fragmented, but I infer that you are asking about evaluating \( h(15) \) for some expression related to Fibonacci sequence or exponential growth. However, given the format appears incomplete, I will demonstrate calculating a typical function such as \( h(x) = kx^2 \).

To find \( h(15) \):

1. If given \( h(x) = k \cdot x^2 \), we need the constant \( k \).
2. If \( k = 5 \) for example, \( h(15) = 5 \cdot 15^2 = 5 \cdot 225 = 1125 \).

Could you confirm the complete function for accurate evaluation?

Question 2: Identifying the Graph of the Linear Equation

Given the equation: \[ y + 1 = 2(x + 3) \] Let's rearrange it to the slope-intercept form (\(y = mx + b\)):

1. Distributing the \(2\): \[ y + 1 = 2x + 6 \]
2. Subtracting 1 from both sides gives: \[ y = 2x + 5 \]

Now you need to find the graph that represents this equation:

• The y-intercept is \(5\).
• The slope is \(2\), meaning that from the point \( (0, 5) \), you'll rise \( 2\) units and run \( 1\) unit to the right.

Check the graph options to see which one meets this criteria.

Question 3: Identifying the Equation of the Quadratic Function

You have mentioned that there is a quadratic function shown in a graph. Let's analyze the options given based on the typical form of quadratic functions:

1. The vertex of the quadratic is typically presented in the form \( y = a(x - h)^2 + k \) where \( (h, k) \) is the vertex.
2. Look for the vertex from the graph you have; if the vertex appears to be at \( (-3, 4) \) with a downward opening (as suggested by a negative lead coefficient).

Among the options: A) \( y = -2(x + 3)^2 + 4 \) (vertex at (-3, 4)) B) \( y = - (x - 3)^2 + 4 \) (vertex at (3, 4)) C) \( y = (x + 3)^2 + 4 \) (vertex at (-3, 4)) D) \( y = 6(x + 3)^2 - 4 \) (opening upwards at (-3, -4))

Based on the downward opening behavior and if the vertex is indeed at \((-3, 4)\), the correct answer would be A.

Question 4: Finding the Range of the Height Function

The equation for the height of a ball dropped from a height is given by: \[ y = -16t^2 + 20 \]

1. Note that the maximum height is \(20\) feet (at \(t = 0\)).
2. As the ball falls, the height \(y\) eventually reaches \(0\) feet when it hits the ground.

The range of the function is:

• The height \(y\) can be from \(0\) (ground level) up to \(20\) (initial drop height).

Thus, the range is \[ 0 \leq y \leq 20 \].

Let me know if there’s any specific part you want to go deeper into or clarify!