Not sure how to do these two questions.
The lines dont seem to exist.
(e) x2 – x – 8 = 0
(f) x2 + x = 4
All you have to do is solve for x in your quadratic equations and then substitute those values into the equation of your respaective line. This will give you the coordinates you seek. We call this in the biz, solving systems of equations.
O.K. Let's find the equation of the line that goes through the points
(-2,0) and (0,2)
By the point slope equation: y – y1 = m(x – x1),
we see that (2-0)=m(0-(-2))
2=2m
m=1
now the slope intercept form: y=mx+b
using a point and the slope =1 we see that
0=-2+b
b=2 so the equation we seek is y=1x+2
Now since y always equals y we solve the system
Is that enough info?
Yes, but how then would you learn?
Try reviewing the solutions and suggestions you've received in various of your threads on this exercise, such as this and this.
For instance, you have been told, for the first equation, to "Think about it! If y = 8 and y = x^2 - x, then x^2 - x = 8, etc." So think about what it means for two lines to be equal or to intersect. Then look at the graph and see how you can relate that to what is given to you in the picture.
You might have to do a little thinking and manipulating, working with the concepts and the provided graphs, to arrive at your answer....
What question are you talking about? Was the problem to solve those equations? I see that you have graphed y= x^2- x and y= 8. The roots of x^2- x- 8= 0 are the x-values where those graphs cross. It looks like one of the roots is between -3 and -2 and the other between 3 and 4. But what do y= x+ 2 and y= -2x+ 4 have to do with this problem?
Hi. I did not draw this graph we were given it to answer about seven questions from. I answered the first 5 fine as I just had to look where they intercept. The other two (above) I think are much harder so I came on here hoping someone would give me the answers to these last two. Thanks!
Use the graphs to find the solutions to:
(e) x2 – x – 8 = 0
(f) x2 + x = 4
Graphs are at top of thread. I really need help with these questions. Thanks. We are suppose to find soloutions to these equations (co-ordinates) of where they intercept. x2 – x refers to the graph y=x2 – x. Thanks
Ahh! Thank you! $\displaystyle x^2- x- 8= 0$ is the same as $\displaystyle x^2- x= 8$ so solutions are the values of x where your graphs of $\displaystyle y= x^2- x$ and $\displaystyle y= 8$ intersect. As I said before they appear to be a value between -3 and -2 and a value between 3 and 4.
For $\displaystyle x^2+ x= 4$, to use the graphs you have, subtract 2x from both sides: $\displaystyle x^2- x= 4- 2x= -2x+ 4$. It looks like those graphs intersect for x between -3 and -2 and x between 1 and 2. If those graphs were on a computer or graphing calculator you could get more accurate values by enlarging the graphs or "zooming" in on the points.
$\displaystyle x^2 - x - 8 = 0 \Rightarrow x^2 - x = 8$.
Geometrically, $\displaystyle x^2 - x = 8$ corresponds to solving $\displaystyle y = x^2 - x$ and $\displaystyle y = 8$ simultaneously. The solution for x in this case is the same as the x-cordinate of the intersection point of the graphs of $\displaystyle y = x^2 - x$ and $\displaystyle y = 8$.
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$\displaystyle x^2 + x = 4 \Rightarrow x^2 - x + 2x = 4 \Rightarrow x^2 - x = -2x + 4$.
Geometrically, $\displaystyle x^2 - x = -2x + 4$ corresponds to solving $\displaystyle y = x^2 - x$ and $\displaystyle y = -2x + 4$ simultaneously. The solution for x in this case is the same as the x-cordinate of the intersection point of the graphs of $\displaystyle y = x^2 - x$ and $\displaystyle y = -2x + 4$.
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In both cases you can read off the x-coordinates of the intersection points using the graphs you've been given.
Hi. Thanks for your reply. I think
I understand now. I can find the intersection points of the equations you have given me. Once I have found them do I have to change the x coordinate to a minus?? E.g 3 = -3, 4 = -4. How about y do I leave this positive or change to negative? Thanks