Question 14

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Jambmaths question: 

Which of the following represent the graph above?

Option A: 

$y=2+7x+4{{x}^{2}}$

Option B: 

$y=2-7x+4{{x}^{2}}$

Option C: 

$y=2+7x-4{{x}^{2}}$

Option D: 

$y=2-7x-4{{x}^{2}}$

Jamb Maths Solution: 

Note: where the curve cut x – axis are the roots of the equation. The roots are –2 and ¼ . Also the graph has maximum value of y =2, therefore, equation will be of the form (–ax2 + bx + c = 0)$\begin{align}  & (x+2)(x-\tfrac{1}{4})=0 \\ & {{x}^{2}}-\tfrac{1}{4}x+2x-\tfrac{1}{2}=0 \\ & {{x}^{2}}+\tfrac{7}{4}x-\tfrac{1}{2}=0 \\ & 4{{x}^{2}}+7x-2=0 \\ & \text{Multiply through by }-1 \\ & -4{{x}^{2}}-7x+2=0 \\\end{align}$

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