Question 401463: How do I graph points (i.e (0,0), (3,-2), (4,-5)) on a coordinate plane?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How do I graph points (i.e (0,0), (3,-2), (4,-5)) on a coordinate plane?
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Remember the form of a quadratic equation:
y=ax^2+bx+c
We do not know whether this is a quadratic equation, but we can try to find a, b, and c, then graph it to find out if it is a quadratic equation.
for coordinates(0,0), 0=a(0^2)+b*0+c
0=c
c=0
for coordinates(3,-2), -2=a(3^2)+3b+c
-2=9a+3b+c
9a+3b+c=-2
for coordinates(4,-5), -5=a(4^2)+4b+c
-5=a(16)+4b+c
16a+4b+c=-5
we now have 3 equations with 3 unknowns, but c=0, so we only have two of the unknowns, a and b, to solve
9a+3b=-2
16a+4b=-5
multiply first equation by 4, and second equation by -3
36a+12b=-8
-48a-12b=+15
-12a=7
a=-7/12
b=(-2-9a)/3
=((-8/4-(9*-7/12))/3
=(-8/4+21/4)/3
=(13/4)/3
b=13/12
we now have an equation which appears to be a parabola.
f(x)=-(7/12)x^2+(13/12)x+0
see the graph below: note the 3 given coordinates,(0,0),(3,-2),and (4,-5) on the curve
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