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Question

Match the following quadratic polynomials with the coordinates of their vertex.

A
(1,2)
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B
(1114,14928)
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C
(13,83)
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D
(29,419)
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Solution

For any quadratic polynomial y=ax2+bx+c, the coordinates of the vertex is given as:
(b2a,D4a)(i)
Now, let's take the quadratic expressions one by one to find it's vertex.
(1). y=5x2+10x+3
On comparing with standard form of quadratic expression y=ax2+bx+c
we get, a=5,b=10,c=3
D=b24ac=(10)2453=40
Substituting the values of a,b & D in (i), we get:
(b2a,D4a)(1025,4045)(1,2)
Hence, the coordinates of vertex is given as:
(1,2).

(2). y=3x22x+3
On comparing with standard form of quadratic expression y=ax2+bx+c
we get, a=3,b=2,c=3
D=b24ac=(2)2433=32
Substituting the values of a,b & c in (i), we get:
(b2a,D4a)((2)23,(32)43)(13,83)
Hence, the coordinates of vertex is given as:
(13,83).

(3). y=7x211x1
On comparing with standard form of quadratic expression y=ax2+bx+c
we get, a=7,b=11,c=1
D=b24ac=(11)247(1)=149
Substituting the values of a,b & c in (i), we get:
(b2a,D4a)((11)27,14947)(1114,14928)
Hence, the coordinates of vertex is given as:
(1114,14928).

(4). y=9x2+4x5
On comparing with standard form of quadratic expression y=ax2+bx+c
we get, a=9,b=4,c=5
D=b24ac=(4)24(9)(5)=164
Substituting the values of a,b & c in (i), we get:
(b2a,D4a)(42(9),(164)4(9))(29,419)
Hence, the coordinates of vertex is given as:
(29,419).

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