I sketched the graph for this but I don't know how to find B and C:
x=t-2
Sketch the graph of: for -2¡Üt¡Ü5
Y=t^2-4t-3
B. State the domain of x and the range of y.
c. Write y as a function of x.
its supposed to say sketch the graph of the x and y and then the -2¡Ýt¡Ý5 should be -2 < (or equal to) t < (or equal to) 5
To find B and C, we need to follow these steps:
Step 1: Determine the graph of y = t^2 - 4t - 3 by substituting different values of t and calculating the corresponding y-values.
Step 2: Sketch the graph on a coordinate system.
Step 3: Analyze the graph to determine the answers to the questions.
Now let's break down the process:
Step 1: Determine the graph of y = t^2 - 4t - 3:
To find the graph, substitute different values of t within the given range (-2 ≤ t ≤ 5) and calculate the corresponding y-values.
For example, when t = -2, we can evaluate y as follows:
y = (-2)^2 - 4(-2) - 3
y = 4 + 8 - 3
y = 9
Similarly, we can find more points:
When t = -1, y = (-1)^2 - 4(-1) - 3 = 10
When t = 0, y = (0)^2 - 4(0) - 3 = -3
When t = 1, y = (1)^2 - 4(1) - 3 = -6
When t = 2, y = (2)^2 - 4(2) - 3 = -5
Continue calculating the y-values for t = 3, 4, and 5.
Step 2: Sketch the graph on a coordinate system:
Using the calculated coordinates, plot these points on a graph with t on the x-axis and y on the y-axis. Connect the points to form a smooth curve.
Step 3: Analyze the graph to determine the answers:
a. The domain of x: Looking at the graph, note that the domain of x (or the t-values) is -2 ≤ t ≤ 5. This means that x takes values between -2 and 5, inclusive.
b. The range of y: Examining the graph, we can see that the range of y is from -6 to 9, inclusive, as these are the minimum and maximum y-values on the graph, respectively.
c. Writing y as a function of x:
To write y as a function of x (or t), you can rearrange the given equation y = t^2 - 4t - 3 to obtain t in terms of x:
t^2 - 4t - 3 - y = 0
Now, you can solve this quadratic equation using methods such as factoring, completing the square, or the quadratic formula to express t as a function of x.