The maximum value of a quadratic function
f
is
−
3
, its axis of symmetry is
x
=
2
and the value of the quadratic function at
x
=
0
is
−
9
. What will be the coefficient of
x
2
in the expression of
f
?
Answers
Answer:
it is so difficult i think and ia am a kid
Given : The maximum value of a quadratic function is - 3
its axis of symmetry is x = 2
value of the quadratic function at x = 0 is - 9
To Find : the coefficient of x²
Solution:
axis of symmetry is x = 2
=> f(x) = a(x - 2)² + c
f' (x) = 2a(x - 2)
f' (x) = 0 => x = 2
f''(x) = 2a < 0 because its maximum value
Hence a is -ve
f(2) = -3
=> -3 = a(2 - 2)² + c
=> -3 = c
Hence f(x) = a(x - 2)² - 3
value of the quadratic function at x = 0 is - 9
=> f(0) = - 9
=> -9 = a( 0 - 2)² - 3
=> -6 = 4a
=> a = -6/4
=> a = - 3/2
f(x) =(-3/2)(x - 2)² - 3
= (-3/2)(x² -4x + 4) - 3
= (-3/2)x² + 6x - 6 - 3
= (-3/2)x² + 6x -9
coefficient of x² = -3/2
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