A tunnel is in the shape of a parabola. if the tunnel is 40 feet wide and has a maximum height of 12 feet. write the equation of the quadratic function that represents the tunnel(let the axis of symmetry be the y-axis)​

So, The tunnel is 40 feet wide & y - axis is the axis of symmetry. This means that starting point and ending point of tunnel will be at (-20,0) and (20,0):

x=−20

AND

x=20

are the roots of this quadratic equation:

The tunnel has a maximum height of 12 feet. This means that top point of tunnel will be (0,12):

When  x=0,y=12.

The quadratic equation will be as follows:

y=ax2+bx+c

(1) Putting point (0,12) =>

12=a(0)2+b(0)+c

=>c=12

(2) Putting point (20,0) =>

0=a(20)2+b(20)+12

400a+20b+12=0  (I)

(3) Putting point (-20,0) =>

0=a(−20)2+b(−20)+12

400a−20b+12=0  (II)

We got Equations (I) & (II). Lets find out ‘a’ and ‘b’:

Add (I) and (II) =>

800a+24=0  (20 b and -20 b got cancelled)

800a=−24

a=−24800

=>a=−0.03

(I)  400(−0.03)−20b+12=0

−>−12+12−20b=0

−>−20b=0

=>b=0

Therefore, the quadratic equation of the tunnel is:

−>y=(−0.03)x2+(0)x+12

=>y=12−0.03x2

Hope you got it :-)

7/2

(decimal: 3.5)

welcome ; )

step-by-step explanation: