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Question

# Select the correct statements for the quadratic polynomial y=x2+5x+6.

A
ymin=52
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B
Graph of y=x2+5x+6 is:
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C
yintercept(0,6)
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D
Vertex (52,14)
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Solution

## The correct option is D Vertex ≡(−52,−14)Given: y=x2+5x+6 On comparing with standard form of quadratic expression y=ax2+bx+c We get: a=1,b=5,c=6 & D=b2−4ac=(5)2−4⋅1⋅6=1 Now, the vertex of the quadratic polynomial is given by: V≡(−b2a,−D4a) Where −b2a=−52.1=−52 & −D4a=−14.1=−14 ∴Vertex≡(−52,−14) Now, y− intercept is given as the value of y for x=0 ⇒y−intercept≡(0,6) We know, for an upward opening parabola, we only have minimum value and that minimum value is at vertex. ∴ymin=−14

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