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Mathematics
Mathematics
Problem
Consider the quadratic function
y
=
x
2
y = x^2
y
=
x
2
. The point
P
(
a
,
a
2
)
P(a, a^2)
P
(
a
,
a
2
)
lies on the function. The line
y
=
m
(
x
−
a
)
+
c
y = m(x - a) + c
y
=
m
(
x
−
a
)
+
c
also passes through P. What, if anything, can you say about the values of
m
m
m
and
c
c
c
? Suppose
y
=
m
(
x
−
a
)
+
a
2
y = m(x - a) + a^2
y
=
m
(
x
−
a
)
+
a
2
touches
y
=
x
2
y = x^2
y
=
x
2
at P. Find the value of
m
m
m
.
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