The lines are more then you think they are
Answer:
f(x) = -(x-3)^2 + 4
Step-by-step explanation:
(h; k) are the coordinates of the vertex.
On the graph are (3, 4), therefore we have:
f(x) = a(x-3)^2 + 4
We have the x- intercept (1,0) -> x=1; y=0.
Substitute them into the equation:
0 = a(1 - 3)^2 + 4
0 = a(-2)^2 + 4
4a + 4 = 0 | -4
4a = -4 |-4
a = -1
So, we have the answer:
f(x) = -(x-3)^2 + 4
Answer: he hiked 5.6 miles up the canyon.
Step-by-step explanation:
Let x represent his speed hiking uphill.
His speed running downhill was 2.8 mph greater than his speed hiking uphill. This means that his speed running downhill would be x + 2.8
Distance = speed × time
Kevin hiked up Lamb’s Canyon in 2 hours. This means that the distance covered by hiking uphill is 2 × x = 2x
He ran back downhill in 1 hour. This means that the distance covered by running downhill is 1 × (x + 2.8) =
x + 2.8
Since the distance uphill is the same as the distance downhill, then
2x = x + 2.8
2x - x = 2.8
x = 2.8
Therefore, the distance hiked up the canyon is
2x = 2 × 2.8 = 5.6 miles
Let’s call the speed of the slower car S, then the speed of the other is S+10mph.
At 5pm they have been travelling for 3 hours. The slower car travels a distance 3S and the faster one 3(S+10).
But the two distances must add up to 240 miles so 3S+3(S+10)=240, 3S+3S+30=240, 6S=210, S=35 mph. The faster car’s speed is 45mph. We can see that 3S is the same distance as 3x, so x=S=35 mph, and the distance the faster car travels is 3×45=135 miles.
This is my answer - a beautiful image. You haven’t attached the image to determine the answer, please do!
