line k has a slop of -5. Line J is perpendicular to line K and passes through the point (5,9). Create the equation for line j.
1 answer:
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A parabolic function's key characteristic is either having 2 x-intercepts or 2 y-intercepts. That is the reason why the standard form of parabolic functions are:
(x-h)^2 = +/- 4a(y-k) or (y-k)^2 = +/- 4a(x-h), where
(h,k) is the coordinates of the vertex
4a is the lactus rectum
a is the distance from the focus to the vertex
This is also called vertex form because the vertex (h,k) is grouped according to their variable.
Since we don't know any of those parameters, we'll just have to graph the data points given as shown in the picture. From this data alone, we can see that the parabola has two x-intercepts, x=-4 and x=-2. Since it has 2 roots, the parabola is a quadratic equation. Its equation should be
y = (x+4)(x+2)
Expanding the right side
y = x²+4x+2x+8
y = x²+6x+8
Rearrange the equation such that all x terms are on one side of the equation
x²+6x+___=y-8+___
The blank is designated for the missing terms to complete the square. Through completing the squares method, you can express the left side of the equation into (x-h)² form. This is done by taking the middle term, dividing it by two, and squaring it. So, (6/2)²=9. Therefore, you put 9 to the 2 blanks. The equation is unchanged because you add 9 to both sides of the equation.
The final equation is
x²+6x+9=y-8+9
(x+3)²=y+1
(x-h)^2 = +/- 4a(y-k) or (y-k)^2 = +/- 4a(x-h), where
(h,k) is the coordinates of the vertex
4a is the lactus rectum
a is the distance from the focus to the vertex
This is also called vertex form because the vertex (h,k) is grouped according to their variable.
Since we don't know any of those parameters, we'll just have to graph the data points given as shown in the picture. From this data alone, we can see that the parabola has two x-intercepts, x=-4 and x=-2. Since it has 2 roots, the parabola is a quadratic equation. Its equation should be
y = (x+4)(x+2)
Expanding the right side
y = x²+4x+2x+8
y = x²+6x+8
Rearrange the equation such that all x terms are on one side of the equation
x²+6x+___=y-8+___
The blank is designated for the missing terms to complete the square. Through completing the squares method, you can express the left side of the equation into (x-h)² form. This is done by taking the middle term, dividing it by two, and squaring it. So, (6/2)²=9. Therefore, you put 9 to the 2 blanks. The equation is unchanged because you add 9 to both sides of the equation.
The final equation is
x²+6x+9=y-8+9
(x+3)²=y+1
Step-by-step explanation:
We have to find the point in the feasible region which maximizes the objective function. To find that point first we need to graph the given inequalities to find the feasible region.
Steps to graph 3x + y ≤ 12:
First we graph 3x + y = 12 then shade the graph for ≤.
plug any value of x say x=0 and x=2 into 3x + y = 12 to find points.
plug x=0
3x + y = 12
3(0) + y = 12
0 + y = 12
y = 12
Hence first point is (0,12)
Similarly plugging x=2 will give y=6
Hence second point is (2,6)
Now graph both points and joint them by a straight line.
test for shading.
plug any test point which is not on the graph of line like (0,0) into original inequality 3x + y ≤ 12:
3(0) + (0) ≤ 12
0 + 0 ≤ 12
0 ≤ 12
Which is true so shading will be in the direction of test point (0,0)
We can repeat same procedure to graph other inequalities.
From graph we see that ABCD is feasible region whose corner points will result into maximum or minimu for objective function.
Since objective function is not given in the question so i will explain the process.
To find the maximum value of objective function we plug each corner point of feasible region into objective function. Whichever point gives maximum value will be the answer
