The gradient of a curve is 2x + 7 and the curve passes through point (2, 0). find the equation of the curve.

  • A \(y = x^2 + 7x + 9\)
  • B \(y = x^2 + 7x - 18\)
  • C \(y = x^2 + 7x + 18\)
  • D \(y = x^2 + 14x + 11\)

The correct answer is B. \(y = x^2 + 7x - 18\)

The gradient of a curve is given by the derivative of the curve. Since the gradient of the curve is 2x + 7, we can find the equation of the curve by integrating the gradient with respect to x:

\(\int (2x + 7) dx = x^2 + 7x + C\)

where C is the constant of integration. To find the value of C, we can use the fact that the curve passes through the point (2, 0). Substituting x = 2 and y = 0 into the equation of the curve, we get:

\(0 = 2^2 + 7(2) + C\)

\(0 = 4 + 14 + C\)

\(C = -18\)

Substituting this value of C back into the equation of the curve, we get:

\(y = x^2 + 7x - 18\)

So, the equation of the curve is \(y = x^2 + 7x - 18\).

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