For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range. The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2. The vertex is (1, 2), the domain is all real numbers, and the range is y ≤ 2. The vertex is (−1, 2), the domain is all real numbers, and the range is y ≥ 2. The vertex is (−1, 2), the domain is all real numbers, and the range is y ≤ 2.

The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2

Step-by-step explanation:

The functions given to us is:

f(x) = 3(x - 1)² + 2

As there is no limitation of x, all value of x are possible. So

Domain = All real numbers

For all values of x, the minimum value of y is 2 calculated at x = 1. The rest of the values are greater than 2. So,

Range = y ≥ 2

Simplifying the function:

f(x) = 3(x² + 1² - 2(x)(1)) + 2

f(x) = 3(x² - 2x + 1) +2

f(x) = 3x² - 6x + 3 + 2

f(x) = 3x² - 6x + 5    (ax² + bx + c)

where a = 3, b = -6, c = 5

x-coordinate of Vertex is given as:

Vertex(x) = -b/2a = 6/2(3)

Vertex(x) = 1

Substitute x=1 in the function, we get

Vertex(y) = 2

So Vertex is at (1,2)

452,489 to the nearest thousand is 452,000

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x