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Answer:
Part 1) The graph in the attached figure
Part 2) Three points that solve the equation could be (-18,0),(0,4.5) and (-2,4)
Step-by-step explanation:
we know that
To graph a line we need to plot two points
If a point solve the linear equation, then the point is a solution of the linear equation
step 1
Find the first point that solve the equation
<em>Find the x-intercept</em>
The x-intercept is the value of x when the value of y is equal to zero
For y=0
The x-intercept is the point (-18,0)
step 2
Find the second point that solve the equation
<em>Find the y-intercept</em>
The y-intercept is the value of y when the value of x is equal to zero
For x=0
The y-intercept is the point (0,4.5)
step 3
With the intercepts graph the line
Plot the intercepts and join the points to graph the line
using a graphing tool
see the attached figure
step 4
Find the third point that solve the equation
Assume a value for x and then solve for y
I assume x=-2
substitute in the linear equation and solve for y
The third point is the point (-2,4)
The change in the water vapors is modeled by the polynomial function c(x). In order to find the x-intercepts of a polynomial we set it equal to zero and solve for the values of x. The resulting values of x are the x-intercepts of the polynomial.
Once we have the x-intercepts we know the points where the graph crosses the x-axes. From the degree of the polynomial we can visualize the end behavior of the graph and using the values of maxima and minima a rough sketch can be plotted.
Let the polynomial function be c(x) = x ² -7x + 10
To find the x-intercepts we set the polynomial equal to zero and solve for x as shown below:
x ² -7x + 10 = 0
Factorizing the middle term, we get:
x ² - 2x - 5x + 10 = 0
x(x - 2) - 5(x - 2) =0
(x - 2)(x - 5)=0
x - 2 = 0 ⇒ x=2
x - 5 = 0 ⇒ x=5
Thus the x-intercept of our polynomial are 2 and 5. Since the polynomial is of degree 2 and has positive leading coefficient, its shape will be a parabola opening in upward direction. The graph will have a minimum point but no maximum if the domain is not specified. The minimum points occurs at the midpoint of the two x-intercepts. So the minimum point will occur at x=3.5. Using x=3.5 the value of the minimum point can be found. Using all this data a rough sketch of the polynomial can be constructed. The figure attached below shows the graph of our polynomial.
