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6.04 Graphing systems of nonlinear equations
Jasmine Rhoden
The equation for this parabola is y = -x^2 + 36.
In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow.
Table
The airplane will cross the rainbow at (-4.9,11.99) and (6,0).
Table & equation of line
The equation of the line is...
Finding the Equation Using Two Points
equation of line solution
Find the slope using
m = (y2-y1)/(x2-x1)
we plug in the intersection points.
m=(0-11.99)/(6-(-4.9))
and that will get us m=-11.99/11.9
which will equal -1
now we plug in m into the slope intercept formula
y=mx+b
y=-1x+b = y=-x+b
Now we'll have to find the y-intercept.
We use one of the point to solve for it. -> (6,0)
0=-1(6)+b So, the y-intercept is 6.
0=-6+b now plug the numbers into
+6 +6 the formula.
6=b y=-x+6
What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not?
the domain and the range of -x^2+36;
range -> (-infinity,36)
domain -> (-infinity, infinity)
the domain represents the values that are possible for (x).
range represents the values that are possible for (y).
the values make mo sense because it can not be graphed.
What are the x- and y-intercepts of the rainbow? Explain what each intercept represents.
the y and x-intercepts of f(x)=-x^2+36;
y-intercepts : (0,36)
x-intercepts : (6,0) (-6,0)
each intercept represent points where functions touch the x and y axis.
Is the linear function you created with your table positive or negative? Explain.
the linear function is negative because it's decreasing.
What are the solutions or solution to the system of equations created? Explain what it or they represent.
the solutions are two points ;
(6,0) and (-4.9,11.99)
these points represents where the rainbow intersects the airplane.
essential questions:
How can graphing be applied to solving systems of nonlinear equations?
you'll find the points of the intersection where those functions intersect when you plot them. then, you can find the answers.
How can constraints be used to model a real-world situation?
constrains can be used as a model.
Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).
y={5x+4/ 3x where the first equation is true if -5<x<2 and the second equation is true if x<2.
For the red line, the segment in between the points is what you want to graph. The points should be solid. This is because it is a "less than or equal to" equation. For the blue line, the segment below the point is what you need to graph. The point should be solid for the same reason as above