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+

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.

the expression (1.26)2t reveals the approximate rate of increases in the number of plants semiannually.

hope this : )