A frog leaps 2 feet horizontally. The highest point in the jump is 1/2 foot. Assume the frog starts at (0,0).what quadratic function models the path of the jump?

The general function is:

+y+=+a%2Ax%5E2+%2B+b%2Ax+

Note that if +x+=+0+ then

+y+=+0+, so that gives you

the point (0,0)

You also are given the point

(2,0), so

+0+=+a%2A2%5E2+%2B+b%2A2+

+4a+=+-2b+

+a+=+-b%2F2+

The formula for the x-coordinate of the

highest point is:

+x%5Bmax%5D+=+-b%2F%282a%29+

By substitution:

+x%5Bmax%5D+=+%28+-b%2F2+%29%2A%28+2%2F%28-b%29%29+

+x%5Bmax%5D+=+1+

+y%5Bmax%5D+=+a%2A1%5E2+%2B+b%2A1+

+y%5Bmax%5D+=+a+%2B+b+

+1%2F2+=+a+%2B+b+

and, since

+a+=+-b%2F2+

+1%2F2+=+-b%2F2+%2B+b+

+1%2F2+=+b%2F2+

+b+=+1+

and

+a+=+-b%2F2+

+a+=+-1%2F2+

So, the equation is:

+y+=+%28-1%2F2%29%2Ax%5E2+%2B+x+

Here is the plot:

+graph%28+400%2C+400%2C+-.5%2C+3%2C+-1%2C+2%2C++%28-1%2F2%29%2Ax%5E2+%2B+x+%29+

Step-by-step explanation:

The general function is:

+y+=+a%2Ax%5E2+%2B+b%2Ax+

Note that if +x+=+0+ then

+y+=+0+, so that gives you

the point (0,0)

You also are given the point

(2,0), so

+0+=+a%2A2%5E2+%2B+b%2A2+

+4a+=+-2b+

+a+=+-b%2F2+

The formula for the x-coordinate of the

highest point is:

+x%5Bmax%5D+=+-b%2F%282a%29+

By substitution:

+x%5Bmax%5D+=+%28+-b%2F2+%29%2A%28+2%2F%28-b%29%29+

+x%5Bmax%5D+=+1+

+y%5Bmax%5D+=+a%2A1%5E2+%2B+b%2A1+

+y%5Bmax%5D+=+a+%2B+b+

+1%2F2+=+a+%2B+b+

and, since

+a+=+-b%2F2+

+1%2F2+=+-b%2F2+%2B+b+

+1%2F2+=+b%2F2+

+b+=+1+

and

+a+=+-b%2F2+

+a+=+-1%2F2+

So, the equation is:

+y+=+%28-1%2F2%29%2Ax%5E2+%2B+x+

Here is the plot:

+graph%28+400%2C+400%2C+-.5%2C+3%2C+-1%2C+2%2C++%28-1%2F2%29%2Ax%5E2+%2B+x+%29+

ok

step-by-step explanation:

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm