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Question

Which of the following is correct for the quadratic polynomial f(x)=2x2+8x12
  1. vertex =(2,20)
  2. f(x)=0 has no real solutions
  3. y intercept =(0,2)
  4. the graph is concave downward 


Solution

The correct option is A vertex =(2,20)
Given quadratic polynomial y=2x2+8x12
where a=2,b=8 and c=12
Since, a>0, so the graph of the given quadratic polynomial is concave upward.
y intercept =(0,c)=(0,12)

D=b24ac   =824×2×(12)=160>0
Real and distinct roots

Vertex
=(b2a,D4a)=(84,1608)=(2,20)  
 

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