Question 1209281
<pre>
Let's plot the points and sketch a parabola through them:

{{{drawing(1950/7,600,-7,6,-15,13, grid(1),
circle(-5,-13,.2),circle(2,7,.2),circle(4,-5,.2),
graph(1950/7,600,-7,6,-15,13,30,(-62/63)x^2+(-2/21)x+(701/63)),
locate(-5,-13,"(-5,-13)"),
locate(2,7,"(2,7)"),
locate(4,-5,"(4,-5)") )}}}

{{{y = ax^2 + bx + c}}}

Substitute each point:

{{{system(-13 = a(-5)^2 + b(-5) + c,
7 = a(2)^2 + b(2) + c,
-5 = a(4)^2 + b(4) + c)}}}

Simplify and put the constants on the right.

{{{system(25a - 5b + c=-13,
4a + 2b + c=7,
16a + 4b + c=-5)}}}

Subtract the 2nd and 3rd equation from the first
to eliminate c

{{{system(21a-7b=-20,9a-9b=-8)}}}

Multiply the 1st by 9 and the 2nd by -7 to eliminate b

{{{system(189a-63b=-180,-63a+63b=56)}}}

Add the equations:

{{{126a=-124}}}

{{{a=-124/126}}}

{{{a=-62/63}}}

Go back to

{{{system(21a-7b=-20,9a-9b=-8)}}}

Multiply the 1st by 9 and the 2nd by -21 to eliminate a

{{{system(189a-63b=-180,-189a+189b=168)}}}

Add the equations:

{{{126b=-12}}}

{{{b=(-12)/126}}}

{{{b=-2/21}}}

Go back to the easiest one of the original
equations:

{{{4a + 2b + c=7}}}

{{{4(-62/63) + 2(-2/21) + c=7}}}

{{{-248/63-4/21+c=7}}}

Multiply through by 63:

{{{-248-12+63c=441}}}

{{{-260+63c=441}}}

{{{63c=701}}}

{{{c=701/63}}}

So {{{abc}}}{{{""=""}}}{{{(-62/63)(-2/21)(701/63)}}}{{{""=""}}}{{{86924/83349}}}

Yes, your teacher should be fired, for they do not know how to teach
mathematics.  No competent teacher would assign such a problem as this!

Edwin</pre>