The gateway arc in st. louis was built in 1965. it is the talles monument in the united states. the arch can be modeled with the function y=0.00635x^2+4x where x and y are in feet.
a. how high above the grounf is the tallest point of the arch?
b. how far apart are the legs of the arch at thier bases?
c. what are the domain and range of this function?

A)  630 feet

B)  630 feet

C)  Domain: [0,630] and Range: [0,630]

Step-by-step explanation:

The gateway arc in St. Louis was built in 1965. It is the tallest monument in the united states.

The modeled of arc,

where x and y are in feet

Part A) The given model is parabolic curve. The highest point at vertex of parabolic curve.

The x-coordinate of maximum height,

where, a is coefficient of x² and b is coefficient of x

a = -0.00635

b = 4

Put x = 314.96 into model to get the value of y

Hence, the tallest point of the arch at 630 feet above ground.

Part B) The distance between the legs of arch is difference of zeros of equation.

Hence, the legs of the arch 630 feet apart to each other.

Part C)

Domain: It is input value of x where function is defined.

Range: It is output value of function for all defined value of x.

For this model, It is a function of arch. So, y value can't be negative.

Therefore,

Domain: [0,630]

Range: [0,630]

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get,   becomes

2. the function is translated 5 units to the right.

so, we get,   becomes

3. the function is translated 5 units upwards.

so, we get,   becomes

4. the function is translated 5 units downwards.

so, we get,   becomes

5. the function is reflected across x-axis.

so, we get,   becomes

6. the function is reflected across y-axis.

so, we get,   becomes .

step-by-step explanation:

mark brainliest.