The parabola is represented with the equation y = (1/4p)(x - h)^2 + k.
That is the vertex form of the equation, because h and k represent the coordinates of the vertex of the parabola, h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
So the vertex is (h, k).
To place it in the graph you just need to know the values of h and k. For example, for a positive value of p, if they k and h are positive, means the vertex is in the first quadrant.
After that the number of zeros will depend on the value of k.
Again assuming p is positive, which implies that the parabola opens upward.
k = 0 means the parabola has one zero, because the vertex is just on the x-axis.
k > 0 means the parabola has none zeros, because the vertex will be above the x-axis and it will not intersect the x - axis.
k < 0 means the parabola has two zeros, because the vertex will be below the x - axis and it will intersect the x -axis at two points.
If p is negative, the parabola opens downward and the conclusions are the opposite
k < 0 the parabola has non zeros.
k > 0 the parabola has two zeros
k = 0 the parabola has one zero (just as when p is positive)
We can used the Simpson's Rule says to approximate the area under a given curve using the following formula:
<span>(Δx/3)[f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + ... + 2f(xn-2) + 4f(xn-1) + f(xn)] </span>
<span>The pool is divided into 8 subintervals. We integrate the given function from 0 to 24, while the graph provides values of f(x) at 7 different points. The first value given, 6.2, is NOT f(0). It is f(3). Using Simpson's Rule, and dividing the lake of 24 meters into 8 subintervals, we write the equation: </span>
<span>area = (3/3)[f(0) + 4f(3) + 2f(6) + 4f(9) +2f(12) + 4f(15) + 2f(18) + 4f(21) + f(24)] </span>
<span>Pool area = 0 + 4(6.2) + 2(7.2) +4(6.8) + 2(5.6) + 4(5.0) +2(4.8) +4(4.8) + 0 = 126.4 m^2 </span>
<span>Rounding to the nearest square meter, the area of the lake is approximately 126 m^2 </span>
Answer:
Step-by-step explanation:
slope=change in y/change in x
one way is t pick 2 points, (x1,y1) and (x2,y2)
the slope is (y2-y1)/(x2-x1)
pick some points
(8,4) and (8,0)
slope=(0-4)/(8-8)=-4/0=undefined
the slope is undefined
there is no slope.
They can take the 30 best abd remove the 20 worst, or remove the 20 best and send on the 39 worst.
