Asked by Lucy
Find the quadratic polynomial whose graph goes through the points (-2,5), (0,5), and (1,11).
f(x)= ______x^2+ ______x+ _______
f(x)= ______x^2+ ______x+ _______
Answers
Answered by
bobpursley
I don't know why teachers assign these, if I got them often, I would make a voodoo doll
start with
f(0)=5=25a+0b+25c for the point (o,5)and
f(-2)=5=4a -10b+25c for the (-2,5) and
f(1)=11 you do it.
Now you have three equations, three unknowns. There are a number of ways to solve these, I am uncertain which ways you have been taught. I would use gaussian elimination on a calculator (see your calculator handbook)
start with
f(0)=5=25a+0b+25c for the point (o,5)and
f(-2)=5=4a -10b+25c for the (-2,5) and
f(1)=11 you do it.
Now you have three equations, three unknowns. There are a number of ways to solve these, I am uncertain which ways you have been taught. I would use gaussian elimination on a calculator (see your calculator handbook)
Answered by
Steve
since f(-2) = f(0), symmetry demands that the vertex be at x = -1. So,
y = a(x+1)^2 + k
Now we have
a+k = 5
4a+k = 11
a = 2
k = 3
so,
y = 2(x+1)^2 + 3
y = a(x+1)^2 + k
Now we have
a+k = 5
4a+k = 11
a = 2
k = 3
so,
y = 2(x+1)^2 + 3
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