Find the zeros of each functions by using a graph and a table. F(x)=x^2+9x+14
1 answer:
Zeroes of a function are the values of x when f(x) = 0
So to find the zeroes of the function from the graph search for the points whose y-coordinates = 0
The y-coordinates of the point = 0, if the points lie on the x-axis
That means the zeroes of the function are the points of intersection between the graph and the x-axis
let us see that in the graph
I will draw it and post it here
From the graph
The graph intersects x-axis at points (-7, 0) and (-2, 0)
Then the zeroes of the function are (-7, 0) and (-2, 0)
Let us make the table
x f(x)
-2 0
-1 6
0 14
1 24
2 36
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The first line through points (-3, 0) and (-4, -1) is the orange line.
The second line, through (1, 1) and (2, -1) is the purple line.
Since they are both shaded below, the intersection of the shaded regions, is the region colored in blue.
Both lines are included, since they are solid lines.
The equation of the first line can be found as follows:
the slope is
, thus, the equation is:
The equation of the second line can be found as follows:
the slope is
,
thus the equation of the second line is :
We have to decide on the direction of the inequality sign, so we pick a point, for example (0, 4) which is not in the colored regions of the lines,
so we write the inequalities so that they do not hold for (0, 4)
line 1:
y≥x+4
4≥0+4=4 is true, so we change the sign and write : y≤x+4
similarly, line 2:
y≤-2x+3
4≤-2*0+3=3, which is not true, so we have the correct direction.
Note that since the lines were solid, we include the equality case:
Answer:
the shaded region is the solution to the system of inequalities:
i) y≤x+4
ii) y≤-2x+3
The second line, through (1, 1) and (2, -1) is the purple line.
Since they are both shaded below, the intersection of the shaded regions, is the region colored in blue.
Both lines are included, since they are solid lines.
The equation of the first line can be found as follows:
the slope is
The equation of the second line can be found as follows:
the slope is
thus the equation of the second line is :
We have to decide on the direction of the inequality sign, so we pick a point, for example (0, 4) which is not in the colored regions of the lines,
so we write the inequalities so that they do not hold for (0, 4)
line 1:
y≥x+4
4≥0+4=4 is true, so we change the sign and write : y≤x+4
similarly, line 2:
y≤-2x+3
4≤-2*0+3=3, which is not true, so we have the correct direction.
Note that since the lines were solid, we include the equality case:
Answer:
the shaded region is the solution to the system of inequalities:
i) y≤x+4
ii) y≤-2x+3
Answer:
x=8/3
y= -20/9
Step-by-step explanation:
4X + 3Y -4 =0
Linear egquations must in
so 4X + 3Y =4
THEN
3X + 9Y = - 12
next use calculator to solve it or you can use traditional way