Question
Question 1 A)Given the function f(x)=x2−5x+7f(x)=x2−5x+7, what would be the value of f(−4)f(−4)?(1 point) Responses 11 11 -21 -21 43 43 -29 -29 Question 2 A)(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. At baseball practice, Matt hit the ball into the outfield. The function h(t)=−16t2+32t+3h(t)=−16t2+32t+3 gives the height h(t)h(t) of the baseball in feet, tt seconds after it is hit. A) What is the value of h(1)h(1)? Response area B) What does h(1.74)h(1.74) represent in context? Response area C) Which value would not be valid in the context of this problem? Response area h(−2)h(−2)The height of the ball 1 second after it is hit.The amount of time it takes for the ball to hit the ground.2.1193The height of the ball 1.74 seconds after it is hit.The time it took the ball to be 1.74 feet above the ground.h(2)h(2)h(0)h(0) Question 3 A)Match each equation with the correct feature.(4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. y=−12(x−4)2+1y=−12(x−4)2+1 y=(x+1)2+4y=(x+1)2+4 y=3(x−4)2−1y=3(x−4)2−1 y=(x+4)2−1y=(x+4)2−1 Maximum at 1Minimum at 4Vertex at (4, -1)Axis of symmetry at x = -4
Question 5 A)(4 points) Select the correct answer for each feature of the following function. y=2x2+4x−1y=2x2+4x−1 A) Vertex: B) Axis of Symmetry: C) Minimum: D) Y-Intercept: Question 6 A)A soccer ball was kicked from the ground with an initial velocity of 56 feet per second and followed the path modeled by the function: h(t)=−16t2+56th(t)=−16t2+56t.(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. The vertex of the ball's path indicates that the ball took Response areaseconds to reach its maximum height of Response area feet. Looking at the graph of this function, we can see that the domain in context to this situation is 0 to 3.5 because the ball Response area. 563.5reaches a maximum height of 3.5 feet.0hits the ground after 3.5 seconds.1.7549
Question 8 A)The length of a frame is 3 inches longer than 2 times the width. Which of the following equations describes the relationship between the width (w) of the frame in inches, and the area (A) in square inches? 2w+3(1 point) Responses A=2(w2+3)A=2(w2+3)cap A is equal to 2 times open paren w squared plus 3 close paren A=6w2A=6w2cap A is equal to 6 w squared A=2w+3A=2w+3cap A is equal to 2 w plus 3 A=2w2+3wA=2w2+3wcap A is equal to 2 w squared plus 3 w
Question 10 A)Match the equation on the left to its equivalent on the right.(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. y=(x−3)2+4y=(x−3)2+4 y=x2+6x+5y=x2+6x+5 y=x2−5x+6y=x2−5x+6 y=x2−6x+13y=x2−6x+13y=(x−2)(x−3)y=(x−2)(x−3)y=(x+3)2−4y=(x+3)2−4
Question 12 A) Compare the functions f(x) and g(x) shown in the table. Which function has a greater y-intercept? x f(x) g(x) -2 0 0 -1 1.25 0.5 0 2.5 1.5 1 5 4.5 2 10 13.5(1 point) Responses f(x)f(x)f of x g(x)g(x)g of x Question 13 A) The table below shows the value of a car ($ in thousands) and the time (in years) since it was purchased. Find the average rate of change in value from years 2 to 4. (1 point) Responses -$3,450 per year -$3,450 per year -$3.20 per year -$3.20 per year -$3,200 per year -$3,200 per year -$6400 per year -$6400 per year Question 14 A)Find the average rate of change over the interval [-3,0] for the function f(x)=x2−2x+4f(x)=x2−2x+4.(1 point) Responses −15−15negative 1 fifth -5 -5 15151 fifth 5 5
Question 5 A)(4 points) Select the correct answer for each feature of the following function. y=2x2+4x−1y=2x2+4x−1 A) Vertex: B) Axis of Symmetry: C) Minimum: D) Y-Intercept: Question 6 A)A soccer ball was kicked from the ground with an initial velocity of 56 feet per second and followed the path modeled by the function: h(t)=−16t2+56th(t)=−16t2+56t.(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. The vertex of the ball's path indicates that the ball took Response areaseconds to reach its maximum height of Response area feet. Looking at the graph of this function, we can see that the domain in context to this situation is 0 to 3.5 because the ball Response area. 563.5reaches a maximum height of 3.5 feet.0hits the ground after 3.5 seconds.1.7549
Question 8 A)The length of a frame is 3 inches longer than 2 times the width. Which of the following equations describes the relationship between the width (w) of the frame in inches, and the area (A) in square inches? 2w+3(1 point) Responses A=2(w2+3)A=2(w2+3)cap A is equal to 2 times open paren w squared plus 3 close paren A=6w2A=6w2cap A is equal to 6 w squared A=2w+3A=2w+3cap A is equal to 2 w plus 3 A=2w2+3wA=2w2+3wcap A is equal to 2 w squared plus 3 w
Question 10 A)Match the equation on the left to its equivalent on the right.(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. y=(x−3)2+4y=(x−3)2+4 y=x2+6x+5y=x2+6x+5 y=x2−5x+6y=x2−5x+6 y=x2−6x+13y=x2−6x+13y=(x−2)(x−3)y=(x−2)(x−3)y=(x+3)2−4y=(x+3)2−4
Question 12 A) Compare the functions f(x) and g(x) shown in the table. Which function has a greater y-intercept? x f(x) g(x) -2 0 0 -1 1.25 0.5 0 2.5 1.5 1 5 4.5 2 10 13.5(1 point) Responses f(x)f(x)f of x g(x)g(x)g of x Question 13 A) The table below shows the value of a car ($ in thousands) and the time (in years) since it was purchased. Find the average rate of change in value from years 2 to 4. (1 point) Responses -$3,450 per year -$3,450 per year -$3.20 per year -$3.20 per year -$3,200 per year -$3,200 per year -$6400 per year -$6400 per year Question 14 A)Find the average rate of change over the interval [-3,0] for the function f(x)=x2−2x+4f(x)=x2−2x+4.(1 point) Responses −15−15negative 1 fifth -5 -5 15151 fifth 5 5
Answers
Answered by
GPT-4o mini
Let's go through each question step-by-step.
### Question 1 A)
Given the function \( f(x) = x^2 - 5x + 7 \):
To find \( f(-4) \):
\[
f(-4) = (-4)^2 - 5(-4) + 7 = 16 + 20 + 7 = 43
\]
**Answer: 43**
---
### Question 2 A)
Given the function \( h(t) = -16t^2 + 32t + 3 \):
**A)** To find \( h(1) \):
\[
h(1) = -16(1)^2 + 32(1) + 3 = -16 + 32 + 3 = 19
\]
**B)** \( h(1.74) \) represents the height of the baseball 1.74 seconds after it is hit.
**C)** The invalid value in the context would be \( h(-2) \) because negative time does not make sense in this scenario.
---
### Question 3 A)
Match each equation with the correct feature.
1. \( y = -12(x - 4)^2 + 1 \): **Minimum at 1**, **Vertex at (4, 1)**, **Axis of symmetry at x = 4**.
2. \( y = (x + 1)^2 + 4 \): **Minimum at 4**, **Vertex at (-1, 4)**, **Axis of symmetry at x = -1**.
3. \( y = 3(x - 4)^2 - 1 \): **Maximum at -1**, **Vertex at (4, -1)**, **Axis of symmetry at x = 4**.
4. \( y = (x + 4)^2 - 1 \): **Minimum at -1**, **Vertex at (-4, -1)**.
---
### Question 5 A)
For the function \( y = 2x^2 + 4x - 1 \):
- **A)** Vertex: Can be found using the formula \( x = -\frac{b}{2a} = -\frac{4}{2(2)} = -1 \). To find y-coordinate:
\[
y(-1) = 2(-1)^2 + 4(-1) - 1 = 2 - 4 - 1 = -3.
\] Thus, the vertex is at (-1, -3).
- **B)** Axis of Symmetry: \( x = -1 \).
- **C)** Minimum: \( -3 \).
- **D)** Y-Intercept: To find, set \( x = 0 \):
\[
y(0) = 2(0)^2 + 4(0) - 1 = -1.
\]
---
### Question 6 A)
For the function \( h(t) = -16t^2 + 56t \):
- **Vertex:**
Using the vertex formula: \( t = -\frac{b}{2a} = -\frac{56}{2(-16)} = 1.75 \) seconds.
The maximum height calculated by plugging \( t = 1.75 \):
\[
h(1.75) = -16(1.75)^2 + 56(1.75) \approx 49 feet.
\]
- **Domain:** The ball reaches a maximum height and then falls back to the ground, so it hits the ground after 3.5 seconds.
---
### Question 8 A)
Length \( l = 2w + 3 \). The area \( A = l \cdot w \):
\[
A = (2w + 3) \cdot w = 2w^2 + 3w.
\]
**Response: A = 2w^2 + 3w.**
---
### Question 10 A)
Match the equations:
1. \( y = (x - 3)^2 + 4 \): **Vertex at (3, 4)**.
2. \( y = x^2 + 6x + 5 \): Factor as \( (x+5)(x+1) \).
3. \( y = x^2 - 5x + 6 \): Factor as \( (x-2)(x-3) \).
4. \( y = x^2 - 6x + 13 \): Does not have real roots.
---
### Question 12 A)
From the given table, calculate \( f(x) \) and \( g(x) \) at \( x=0 \):
- \( f(0) = 2.5 \)
- \( g(0) = 1.5 \)
**Response: f(x)** has a greater y-intercept.
---
### Question 13 A)
To find the average rate of change from year 2 to 4, we need values \( V(2) \) and \( V(4) \).
Assuming you have the values from the table:
\[
\text{Average rate of change} = \frac{V(4) - V(2)}{4-2}.
\]
---
### Question 14 A)
For \( f(x)=x^2-2x+4 \):
\[
f(-3) = 9 + 6 + 4 = 19, \quad f(0) = 0 - 0 + 4 = 4
\]
\[
\text{Average rate of change} = \frac{4 - 19}{0 - (-3)} = \frac{-15}{3} = -5.
\]
**Response: -5**
---
Let me know if you need further clarifications or any additional questions!
### Question 1 A)
Given the function \( f(x) = x^2 - 5x + 7 \):
To find \( f(-4) \):
\[
f(-4) = (-4)^2 - 5(-4) + 7 = 16 + 20 + 7 = 43
\]
**Answer: 43**
---
### Question 2 A)
Given the function \( h(t) = -16t^2 + 32t + 3 \):
**A)** To find \( h(1) \):
\[
h(1) = -16(1)^2 + 32(1) + 3 = -16 + 32 + 3 = 19
\]
**B)** \( h(1.74) \) represents the height of the baseball 1.74 seconds after it is hit.
**C)** The invalid value in the context would be \( h(-2) \) because negative time does not make sense in this scenario.
---
### Question 3 A)
Match each equation with the correct feature.
1. \( y = -12(x - 4)^2 + 1 \): **Minimum at 1**, **Vertex at (4, 1)**, **Axis of symmetry at x = 4**.
2. \( y = (x + 1)^2 + 4 \): **Minimum at 4**, **Vertex at (-1, 4)**, **Axis of symmetry at x = -1**.
3. \( y = 3(x - 4)^2 - 1 \): **Maximum at -1**, **Vertex at (4, -1)**, **Axis of symmetry at x = 4**.
4. \( y = (x + 4)^2 - 1 \): **Minimum at -1**, **Vertex at (-4, -1)**.
---
### Question 5 A)
For the function \( y = 2x^2 + 4x - 1 \):
- **A)** Vertex: Can be found using the formula \( x = -\frac{b}{2a} = -\frac{4}{2(2)} = -1 \). To find y-coordinate:
\[
y(-1) = 2(-1)^2 + 4(-1) - 1 = 2 - 4 - 1 = -3.
\] Thus, the vertex is at (-1, -3).
- **B)** Axis of Symmetry: \( x = -1 \).
- **C)** Minimum: \( -3 \).
- **D)** Y-Intercept: To find, set \( x = 0 \):
\[
y(0) = 2(0)^2 + 4(0) - 1 = -1.
\]
---
### Question 6 A)
For the function \( h(t) = -16t^2 + 56t \):
- **Vertex:**
Using the vertex formula: \( t = -\frac{b}{2a} = -\frac{56}{2(-16)} = 1.75 \) seconds.
The maximum height calculated by plugging \( t = 1.75 \):
\[
h(1.75) = -16(1.75)^2 + 56(1.75) \approx 49 feet.
\]
- **Domain:** The ball reaches a maximum height and then falls back to the ground, so it hits the ground after 3.5 seconds.
---
### Question 8 A)
Length \( l = 2w + 3 \). The area \( A = l \cdot w \):
\[
A = (2w + 3) \cdot w = 2w^2 + 3w.
\]
**Response: A = 2w^2 + 3w.**
---
### Question 10 A)
Match the equations:
1. \( y = (x - 3)^2 + 4 \): **Vertex at (3, 4)**.
2. \( y = x^2 + 6x + 5 \): Factor as \( (x+5)(x+1) \).
3. \( y = x^2 - 5x + 6 \): Factor as \( (x-2)(x-3) \).
4. \( y = x^2 - 6x + 13 \): Does not have real roots.
---
### Question 12 A)
From the given table, calculate \( f(x) \) and \( g(x) \) at \( x=0 \):
- \( f(0) = 2.5 \)
- \( g(0) = 1.5 \)
**Response: f(x)** has a greater y-intercept.
---
### Question 13 A)
To find the average rate of change from year 2 to 4, we need values \( V(2) \) and \( V(4) \).
Assuming you have the values from the table:
\[
\text{Average rate of change} = \frac{V(4) - V(2)}{4-2}.
\]
---
### Question 14 A)
For \( f(x)=x^2-2x+4 \):
\[
f(-3) = 9 + 6 + 4 = 19, \quad f(0) = 0 - 0 + 4 = 4
\]
\[
\text{Average rate of change} = \frac{4 - 19}{0 - (-3)} = \frac{-15}{3} = -5.
\]
**Response: -5**
---
Let me know if you need further clarifications or any additional questions!
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