Which statement describes the graph of f(x) = x² - 6x + 9?
1 answer:
Answer:
A parabola with an x-intercept of (3, 0)
Step-by-step explanation:
We can immediately rule out the first and third options, because the equation of a second degree function is a parabola.
Your equation is
ƒ(x) = x² - 6x + 9 = 0
We can factor this equation as
ƒ(x) = (x - 3)²
The parent parabola, y = x², has its x-intercept at (0,0).
Your function subtracts three from x, so the intercept is shifted three units to the right.
The graph of your function is a parabola with an x-intercept of (3, 0).
The figure below shows the graph of your function shifted three units by subtracting three from x.
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Complete question:
Anty was riding his bike to school at a speed of 12 mph. When he was <u>half </u>of the way there, he got a flat tire. His mother drove him the rest of the way at a speed of 48 mph. What was his average speed?
Answer:
His average speed is 19.2 mph
Step-by-step explanation:
Given;
speed of Anty to school half of the way, v₁ = 12 mph
speed of Anty when his mother drove him half of the way, v₂ = 48 mph
The average speed of Anty is calculated as;
The value of the average speed is closer to 12 mph than 48 mph because Anty spent more time moving at 12 mph than at 48 mph.
Let the equal distance travel at each speed = 96 miles
Time taken at 12 mph =
Time taken at 12 mph =
Average speed =
Also, you can assume any other equal distance traveled at each speed, the average speed will still be 19.2 mph.
<u>Check:</u> let the equal distance traveled at each speed = 480 miles
Time taken at 12 mph = 480/12 = 40 hours
Time taken at 48 mph = 480/ 48 = 10 hours
Average speed = (480 + 480) / (40 + 10)
= 19.2 mph