Maths-
General
Easy

Question

The adjoining figure shows the graph of y equals a x to the power of 2 end exponent plus b x plus c Then –

  1. a > 0    
  2. b > 0, c > 0    
  3. c < 0    
  4. b to the power of 2 end exponent less than 4 a c    

hintHint:

So in this question, we have a graph given and we have to do it. As we can see the curve and it is of the parabola and by using the properties of the parabola and its equation, we can answer these questions easily.

The correct answer is: b > 0, c > 0



    The adjoining figure shows the graph of y equals a x to the power of 2 end exponent plus b x plus c
    The given parabola is open downwards that means coefficient ofx squared space less than space 0.
    rightwards double arrow a space less than space 0
    At x = 0, y > 0 ( From graph)
    rightwards double arrow y equals a left parenthesis 0 right parenthesis squared plus b left parenthesis 0 right parenthesis plus c space greater than space 0 space left parenthesis space A t space x space equals space 0 right parenthesis

rightwards double arrow c space greater than space 0
    x coordinates of vertex = negative fraction numerator b over denominator 2 a end fraction > 0 ( From the graph)
    rightwards double arrow negative fraction numerator b over denominator 2 a end fraction space greater than space 0

S i n c e space a space less than space 0

rightwards double arrow b space greater than space 0

    Thus, b > 0, c > 0 is the correct answer.

    Here we can see that the graph was given to us and us to take out the conclusion from that since we have the options available so I would suggest you to always start to check from the options because by the use of options we can see how easily we concluded this question.

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