Janelle says that lines l and m are skew lines. is janelle correct? yes, because the lines are not parallel. yes, because the li
2 answers:
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let's calculate it step by step.
I'll assume that the function we look for is quadratic, because we only got 3 points
I plotted the 3 points for checking the equation later, and some intuited insight. see screenshot 1
let's write the general form of quadratic equations:
f(x) = a*x² + b*x + c
our goal is to correctly determine a, b and c
since we know from the 2nd point that
f(0) = a*0² + b*0 + c = 4
we can say
<em><u>c = 4</u></em>
this one comes almost for free
now to the next point, the 3rd one
f(1) = a*1² + b*1 + 4 = -3
we can write it as
a + b + 4 = -3
we can rearrange that to
<em><u>a = -b -7</u></em>
lastly, to the first point
f(-2) = a*(-2)² + b*(-2) + 4 = 5
simplified to
4a -2b + 4 = 5
since sort of defined a, let's plug it into our newest equation
4*(-b-7) -2b +4 = 5
we just swapped a for what its equal to.
now we just got numbers and b's
simplify it to
-4b -28 -2b +4 = 5
-6b -24 = 5
-6b = 29
<em><u>b = -29/6</u></em>
now we use the exact value of b to plug it into the rather simple equation from earlier. into this one
a = -b -7
a = -(-29/6) -7
a = 29/6 -42/6
<em><u>a= -13/6</u></em>
now that we got a, b and c we can write the whole equation
<em><u>f(x) = -13/6*x² -29/6*x +4</u></em>
see the graphic check in screenshot 2
second part of the problem:
if we want to move the whole graph 4 units down, we effectivly just cancel the +4 part
g(x) = f(x) -4 = f(x) = -13/6*x² -29/6*x +4 -4
<em><u>g(x) = -13/6*x² -29/6*x</u></em>
see screenshot 3 for the graph
So when you're solving for x here and distribute 8 on the right side, it would look like this:
Now in order to solve for x, we know we have to get all the x's on one side of the equal sign. Let's get all our x's to the left side. Since the right side has a positive 8x, you need to subtract 8x on the right. But whatever you do to one side you must do to the other. So since we are subtracting 8x on the right, we need to do that on the left.
But we can't! Since both sides will cancel out to zero before x can be solved.
Therefore the answer is 0.
Hope that helps!