The gradient of a curve is 2x + 7 and the curve passes through point (2, 0). find the equation of the curve.
Answer Details
To find the equation of the curve, we need to integrate the gradient. Since the gradient is 2x + 7, the equation of the curve will be of the form y = x^2 + 7x + C, where C is a constant of integration.
We can find the value of C by using the fact that the curve passes through the point (2, 0). Substituting x = 2 and y = 0 into the equation, we get:
0 = 2^2 + 7(2) + C
0 = 4 + 14 + C
C = -18
Therefore, the equation of the curve is y = x^2 + 7x - 18. The answer is.