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An engineer is designing an arch-shaped gate for the entrance to an amusement park. the gate must be 80 feet wide and 25 feet tall. what will be the equation of the parabolic shape of the gate? a. x2 = -16(y − 25) b. (x − 16)2 = -4(y − 25) c. x2 = -64(y − 25) d. (x − 25)2 = -16(y − 16) e. x2 = -40(y − 25)

Sagot :

The equation of the parabolic shape of the gate is:

(x - 40)² = -64(y - 25)

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

The vertex is at the middle of the parabola, that is, a width of 80/2 = 40 meters and a height of 25 meters, hence h = 40, k = 25, and the equation is:

y = a(x - h)² + k

y = a(x - 40)² + 25

When x = 0, y = 0(start of the arc), hence the leading coefficient is found as follows:

0 = 1600a + 25

a = -25/1600

a = -1/64.

Hence the equation is:

y = -1/64(x - 40)² + 25

(x - 40)² = -64(y - 25)

More can be learned about the equation of a parabola at https://brainly.com/question/17987697

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