SOLUTION: 24. From the list of plotted points (-5,5) (3,5) (-4, 3/2) (2, 3/2) (-3,-1) (1,-1) (-2, -5/2) (0, -5/2) (-1,-3) Form an equation after plotting these points and then answ

Algebra ->  Graphs -> SOLUTION: 24. From the list of plotted points (-5,5) (3,5) (-4, 3/2) (2, 3/2) (-3,-1) (1,-1) (-2, -5/2) (0, -5/2) (-1,-3) Form an equation after plotting these points and then answ      Log On


   

Question 148405: 24. From the list of plotted points

(-5,5) (3,5)
(-4, 3/2) (2, 3/2)
(-3,-1) (1,-1)
(-2, -5/2) (0, -5/2)
(-1,-3)
Form an equation after plotting these points and then answer the questions below:
Is the degree of the polynomial odd or even?
Is the leading coefficient of the polynomial positive or negative?
Number of zeros
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If we plot the points we get

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Now draw a curve through these points to get the equation:

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From the graph, we can see that the degree is even (since both ends of the graph go in the same y direction). Also, we can see that the leading coefficient is positive (since the graph opens upward). Finally, we can see that there are two zeros (since there are two x-intercepts).

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Since we have all of this info, we don't need the equation. However, if you do need the equation, this is how you would find it:

From the graph, we can see that the vertex is (-1,-3).


y=a%28x-h%29%5E2%2Bk Start with the general vertex equation.


y=a%28x--1%29%5E2-3 Plug in h=-1 and k=-3


y=a%28x%2B1%29%5E2-3 Simplify.

Now let's plug in another point. Let's plug in (1,-1)

-1=a%281%2B1%29%5E2-3 Plug in x=1 and y=-1


-1=a%282%29%5E2-3 Add


-1=4a-3 Square 2 to get 4.


0=4a-3%2B1 Add 1 to both sides.


-4a=-3%2B1 Subtract 4a from both sides.


-4a=-2 Combine like terms on the right side.


a=%28-2%29%2F%28-4%29 Divide both sides by -4 to isolate a.


a=1%2F2 Reduce.

So this means that the equation is y=%281%2F2%29%28x%2B1%29%5E2-3

y=%281%2F2%29%28x%5E2%2B2x%2B1%29-3 FOIL


y=%281%2F2%29x%5E2%2B%281%2F2%292x%2B%281%2F2%291-3 Distribute


y=%281%2F2%29x%5E2%2Bx%2B1%2F2-3 Multiply


y=%281%2F2%29x%5E2%2Bx-5%2F2 Combine like terms.


So the equation that goes through the points is y=%281%2F2%29x%5E2%2Bx-5%2F2

From the equation, we can see that the degree of the polynomial is even. Also, we can see that the leading coefficient is positive since a=1%2F2. Finally, if we use the quadratic formula, we'll find that the polynomial y=%281%2F2%29x%5E2%2Bx-5%2F2 has 2 zeros.