The parabolic motion is an illustration of a quadratic function
The equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31
<h3>How to model the function?</h3>
Given that:
x stands for time and y stands for height in feet
So, we have the following coordinate points
(x,y) = (5,0), (11,0) and (10,80)
A parabolic motion is represented as:
y =ax^2 + bx + c
At (5,0), we have:
25a + 5b + c = 0
c= -25a - 5b
At (11,0), we have:
121a + 11b + c = 0
Substitute c= -25a - 5b
121a + 11b -25a - 5b = 0
Simpify
96a + 6b = 0
At (10,80), we have:
100a + 10b + c = 80
Substitute c= -25a - 5b
100a + 10b - 25a -5b = 80
75a -5b = 80
Divide through by 5
15a -b = 16
Make b the subject
b = 15a + 16
Substitute b = 15a + 16 in 96a + 6b = 0
96a + 6(15a + 16) = 0
Expand
96a + 90a + 96 = 0
This gives
186a = -96
Solve for a
a = -16/31
Recall that:
b = 15a + 16
So, we have:
b = -15 * 16/31 + 16
b =-240/31 + 16
Take LCM
b =(-240 + 31 * 16)/31
[tex]b =256/31
Also, we have:
c= -25a - 5b
This gives
c= 25*16/31 - 5 * 256/31
Take LCM
c= -880/31
Recall that:
y =ax^2 + bx + c
This gives
y = -16/31x^2 + 256/31x - 880/31
Hence, the equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31
Read more about parabolic motion at:
brainly.com/question/1130127
If you're asking how to simplify, then this is how you do it.
when a power meets another power but in brackets, then you have to multiply the powers. ¼ × 4 would be 1. i simplified 81 to 3⁴.
The slope intercept form of a line is y = mx + b
Plug in the slope, 6, into m.
Rewrite the equation;
- y = 6x + b
- We need to find b, your y-intercept, to finish this equation.
Plug in your point coordinate, (x, y) ⇒ (-12, -14) into the equation.
Solve for b to find the y-intercept.
Your new equation (your answer) is<em> </em>y = 6x + 58.
First, plug in the given point into y=mx +b to find b (the y-intercept of the line). Use the same slope (m) in the equation since parallel lines have the same slope (3 in this case).
-1 = 3(4) +b
-1 = 12 + b Subtract 12 to both sides.
-13 = b
Now, put your m and b into y=mx+b.
The final answer/equation of your line is:
y=3x -13
