Answer: Vertex : Maximum (2, 0)
Rules:
- (x + d)² = x² + 2dx + d² and (x - d)² = x² - 2dx + d²
- x² + 2dx = (x + d)² - d² and x² - 2dx = (x - d)² - d²
Solve:
x² - 4x + 4
x² - 2(2x) + 2²
(x - 2)²
Into vertex form: a(x - h)² + k
1(x - 2)² + 0
Identify:
vertex : (h, k) = (2, 0)
Find additional things, to graph the equation:
(i) x-intercept: (2, 0)
(ii) y-intercept: (0, 4)
Graph shown:
Answer:
Mai lives 384 miles away from the mountains
Step-by-step explanation:
Let d represent distance between Mai's house and mountains and r represent Mai's rate while going to mountains.
We have been given that there was heavy traffic on the way there, and the trip to mountains took 8 hours.


We are also told that when Mai drove home, there was no traffic and the trip only took 6 hours. Her average rate was 16 miles per hour faster on the trip home.

Upon equating equation (1) and equation (2), we will get:






Upon substituting
in equation (1), we will get:

Therefore, Mai lives 384 miles away from the mountains.
It helps demonstrate it since it forms a right triangle in the middle with 2 base lengths and a hypotenuse. The areas of the squares can be plugged into the pythagorean theorem in order to find the answer