Respuesta :
Answer:
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+
Given the vertex, it is found that the quadratic model is given by:
[tex]f(x) = -\frac{1}{8}(x - 2)^2 + \frac{1}{2}[/tex]
The equation of a parabola with vertex (h,k) is given by:
[tex]f(x) = a(x - h)^2 + k[/tex]
In this problem:
- Leaps 2 feet horizontally, thus the x-coordinate of the vertex is 2, that is, [tex]h = 2[/tex].
- The highest point is half a foot, thus the y-coordinate of the vertex is [tex]\frac{1}{2}[/tex], that is, [tex]k = \frac{1}{2}[/tex].
Then:
[tex]f(x) = a(x - 2)^2 + \frac{1}{2}[/tex]
Starts at (0,0), that is, when [tex]x = 0, y = 0[/tex], and this is used to find a.
[tex]0 = a(0 - 2)^2 + \frac{1}{2}[/tex]
[tex]4a = -\frac{1}{2}[/tex]
[tex]a = -\frac{1}{8}[/tex]
Then, the equation is:
[tex]f(x) = -\frac{1}{8}(x - 2)^2 + \frac{1}{2}[/tex]
A similar problem is given at https://brainly.com/question/17987697
