Question 499336: how do i sketch f(x)=x squared - 5x-6
how do i give an equation for the line of symmetry of the graph. how do i estimate the cordinates if the lowest point on the graph
Found 2 solutions by oberobic, MathLover1:
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Factor
(x-6)(x+1) = x^2 +x -6x = 6
= x^2 -5x -6
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x = 6 or x = -1
These are the x-intercepts: (0,-1), (0,6).
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The y-intercept occurs where x=0.
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y = x^2 -5x -6
So when x=0, y =-6
(0,-6)
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The axis of symmetry = -b/2a
-b/2a = -(-5)/2 = 2.5
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The line of symmetry will go through the lowest point.
y = (2.5)^2 -5(2.5) -6
y = 6.25 -12.5 -6
y = -12.25
The lowest point will be (2.5, -12.25).
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Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website!  or 
The general form of a quadratic is " ".
For graphing, the leading coefficient " " indicates how " " or how " " the  will be.
For |a| >  (such as  or  ), the parabola will be "", because it  more  (three times as fast or four times as fast, respectively, in the case of our sample values of a).
For | a | < (such as  or  ), the parabola will be "", because it more  (one-third as fast or one-fourth as fast, respectively, in the examples).
Also, if is  , then the parabola is  .
In your case, is  and the parabola is  .
If the quadratic is written in the form  (the vertex form), then the vertex is the point ( ,  ).
For a given quadratic , the vertex (, ) is found by computing  , and  .
In your case, , the vertex (, ) will be:
so,
the vertex (, ) is at ( ,  )
the " of  "
If you look at a parabola, you'll notice that you could  a  line right up through the middle which would split the parabola into two mirrored halves. This vertical line, right  the  , is called the of .
If you're asked for the axis, write down the line " ", where is just the  of the vertex. So in the example above, then the axis would be the vertical line  .
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