Question

Consider a quadratic function
f
(
x
)
=
a
x
2
+
b
x
+
5
, and
(
3
,
2
)
is the vertex of
f
. Then choose the correct options.

f
(
x
)
=
x
2
−
4
x
+
5

f
(
x
)
=
1
3
x
2
−
2
x
+
5

f
(
x
)
=
−
2
x
2
−
5
x
+
5

f
(
x
)
=
−
2
3
x
2
+
x
+
5​

Answer 1

Given : a quadratic function

Vertex ( 3 , 2)

To Find :  Correct option

Solution:

f(x) = ax² + bx  + c

vertex is ( 3 , 2)

f(x) = ax² + bx  + c

f'(x) = 2ax  + b

2ax  + b = 0

=> x = - b/2a

Vertex is  3 , 2

=> 3 = - b/2a

=> b = - 6a

which is  (1/3)x² - 2x  + 5  

also x = 3

=> 3 - 6 + 5 = 2   hence y is also satisfied

f(x) = (1/3)x² - 2x  + 5   is correct answer

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