Question 2688: Use the equation y=x(squared)-3x-10
-compared to the graph of y=-3x(squared), does this graph open in the same direction or opposite?
-find x-intercepts for the graph
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could you please answer as soon as possible and please explain how you got your answer and why it is correct...thank you so much!
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! y=x^2-3x-10 -compared to the graph of y=-3x^2,
does this graph open in the same direction or opposite?
-find x-intercepts for the graph
At first you should know how to type the squares correctly.
Use complete square to y=x^2-3x-10, we have
y = (x-3/2)^2 -10 -9/4 = (x-3/2)^2 -49/4 or
y + 49/4 = (x-3/2)^2
So, this parabola has vertex (3/2,-49/4) and open upward (since (x-3/2)^2 >=0)
Another graph y=-3x^2 has vertex (0,0) and open downward (since -3x^2 <=0)
Also, set y=0, in y=x^2-3x-10 =0,
By factoring x^2-3x-10 = (x-5)(x+2) =0, we have x=5 or -2.
So, y=x^2-3x-10 has two x-intercepts 5 ,-2.
Clearly, set y=0, in y=-3x^2, we have the x-intercept =0.
Graphs as below:
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