The path followed by a roller coaster as it climbs up and descends down from a peak can be modeled by a quadratic function, where h(x) is the height, in feet, and x is the horizontal distance, also in feet. The path begins and ends at the same height, covers a total horizontal distance of 100 feet, and reaches a maximum height of 250 feet. Which of the functions could be used to model this situation?

Step-by-step explanation:

Because this quadratic equation would have the curve-down form of:

where a and b are positive coefficient.

If we let the peak (250 ft) of the curve be at x = 0. Then

Also at the begins and ends, thats where y = 0, the 2 points are separated by 100 ft. So let the begin at -50 ft and the end at 50ft. We have

Therefore, the model quadratic equation of our path would be

answer: the first graph

step-by-step explanation:

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc