Hope this helps <span>1) </span><span>Equations with negative values for a</span><span> produce graphs that open down and equations with a positive values for a</span> produce graphs that open up.
<span>2)<span> </span></span><span>As the absolute value of a gets larger our graphs become more narrow (they shoot towards positive or negative infinity faster). This is more interesting than it might appear. If you consider the second derivative of any quadratic it will be the a</span><span> value. The second derivative represents acceleration, so the larger the a value the faster the increase of velocity and accordingly a quicker progression towards positive or negative infinity. Check this out in graphing calculator, press play to vary the value of a from -20 to 20. Notice that when the value of a approaches zero, the approximates a line, and of course when a is 0 we have the line y</span><span> = 2x</span><span> – 1.</span>
Let's follow the transformations that happen to A, to get to A' and A''.
Point A is at (-5, -2)
It moves to (-5, 2) which is where A' is located. Note the x coordinate stays the same while the y coordinate flips from negative to positive. This must mean we applied a reflection over the x axis.
That rule in general is 
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Now compare A'(-5,2) and A''(1,4). We can shift A' 6 units to the right and then 2 units up so we move from A' to A''.
Algebraically this is stated as 
Whatever the x coordinate is, add 6 to it. For the y coordinate, we add on 2.
Applying that rule to B'(-1,2) gets us to

which is the proper location of B''
The same applies to moving C' to C''

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In summary, we started off by reflecting over the x axis. Then we applied the translation rule of "shift to the right 6 units, shift up 2 units".
In terms of algebra, combining the rules
and
will have us end up with 
It would be 110 miles. 5×20=100 and half of 20 is 10