Find the Mean Proportional
If x is the mean proportional between 4 and 9, solve x^2 = 36.
Equation
y = x^2 - 2*9
Graph
Table
| x | y |
|---|---|
| 1 | -17 |
| 2 | -14 |
| 3 | -9 |
| 4 | -2 |
| 5 | 7 |
| 6 | 18 |
| 7 | 31 |
| 8 | 46 |
| 9 | 63 |
| 10 | 82 |
What this lesson covers
What you do
You shape the function y = x^2 - a*b and watch the graph answer.
Challenges to clear
- Set a = 4 and b = 9 — the two numbers of the proportion 4 : x = x : 9.
- Verify your result. The mean proportional x=6 creates the proportion 4:6 = 6:9. Both ratios simplify to 2/3. Confirm that at x=6, the function y is exactly 0.
- A new proportion a : x = x : 8. Slide b to 8 — the far end of it.
- Now find a so that 4 is the mean proportional: 4² must equal a × 8. Check y hits exactly 0 at x = 4.
Check yourself
Why do we choose x = 6 and not x = -6 for the mean proportional?
If a=2 and b=8, what is the mean proportional x?
- Mean proportionals represent ratios of positive quantities, so the value must be positive. — correct
- Because -6 squared is -36.
- Because 6 is the only number whose square is 36.
- Because negative numbers cannot be used in proportions.
- 4 — correct
- 10
- 16
- 5