Question
Use the table to answer the question.
Table of Vertical and Horizontal Distances for Car Headlight Path
Vertical Distance (feet) Horizontal Distance (feet)
1.3 16
0.1 4.2
0 6
0.1 7.8
1.3 0
The table represents the path of light from a car’s headlight. Using technology, create an equation to model the situation. In the equation, what is the value of h? Round to the nearest hundredth.
(1 point)
In the equation that models this situation,
h
=
.
Table of Vertical and Horizontal Distances for Car Headlight Path
Vertical Distance (feet) Horizontal Distance (feet)
1.3 16
0.1 4.2
0 6
0.1 7.8
1.3 0
The table represents the path of light from a car’s headlight. Using technology, create an equation to model the situation. In the equation, what is the value of h? Round to the nearest hundredth.
(1 point)
In the equation that models this situation,
h
=
.
Answers
GPT-4o mini
To model the path of light from a car's headlight using the provided data, we can use a quadratic function of the form:
\[ y = ax^2 + bx + c \]
where \( y \) is the vertical distance (height of the light), and \( x \) is the horizontal distance. We can use the data points from the table to create this model.
The data points from the table are:
1. (16, 1.3)
2. (4.2, 0.1)
3. (6, 0)
4. (7.8, 0.1)
5. (0, 1.3)
To find the best-fit quadratic equation, we can apply quadratic regression using these points.
However, to find just the value of \( h \) from the equation of the best fit, we typically extract the value of \( c \) when the horizontal distance \( x = 0 \).
From the table, when \( x = 0 \), \( y = 1.3 \). Thus, in a standard form of the quadratic equation or line representing this light path, \( h \), which often represents the height at which the light is emitted when \( x = 0 \), is indeed:
\[ h = 1.3 \]
Thus, rounding to the nearest hundredth:
\[
h = 1.30
\]
So, the answer is:
\[
h = 1.30
\]
\[ y = ax^2 + bx + c \]
where \( y \) is the vertical distance (height of the light), and \( x \) is the horizontal distance. We can use the data points from the table to create this model.
The data points from the table are:
1. (16, 1.3)
2. (4.2, 0.1)
3. (6, 0)
4. (7.8, 0.1)
5. (0, 1.3)
To find the best-fit quadratic equation, we can apply quadratic regression using these points.
However, to find just the value of \( h \) from the equation of the best fit, we typically extract the value of \( c \) when the horizontal distance \( x = 0 \).
From the table, when \( x = 0 \), \( y = 1.3 \). Thus, in a standard form of the quadratic equation or line representing this light path, \( h \), which often represents the height at which the light is emitted when \( x = 0 \), is indeed:
\[ h = 1.3 \]
Thus, rounding to the nearest hundredth:
\[
h = 1.30
\]
So, the answer is:
\[
h = 1.30
\]