HELP ASAP - calculating the gradient of the tangent

Question

the original equation is ax²+bx+c between the points A(0,35) and B(8,15), (A, is also 10degrees below the horizontal don't know if this is relevant) and need to calculate the gradient of the tangent at point A(0,35)

then i need to show that b=-0.1763 and thus the values of a,b, and c

then i also need to find the gradient of the tangent between the points (B(8,15) and C(11,15)) with the original equation dx²+ex+f

Answer 1

For an x-y plot, the gradient equals the slope which is the derivative. Also, remember in calculus all angles must be expressed in radians.

To find b: We have f(x) = ax2 + bx + c. Thus f’(x) = 2ax + b. For point A, x = 0, so the value of the derivative f’(0) = b = 10 degrees below horizontal. Thus b = -10 degrees = -0.1745 radians. (-10 x pi / 180).

To find a and c: First plug in the point A(0,35) into your equation to get c = 35. Then use point B to solve for a: 15 = a(8²) - 0.1745(8) + 35, a = -0.2907

For the second problem, we’re missing information. Two points alone cannot define a second degree equation unless we have a gradient or slope at a given point, in which case it could be solved using a similar approach.