If the slope of parabola 𝑦=𝐴𝑥2+𝐵𝑥+𝐶y=Ax 2 +Bx+C, where 𝐴,𝐵,𝐶∈𝑅A,B,C∈R at points (3, 2) and (2, 3) are 16 and 12 respectively.Calculate the value of 𝐴A.
Question
Solution 1
The slope of a parabola y = Ax^2 + Bx + C at a point (x, y) is given by the derivative of the function, which is 2Ax + B.
Given that the slopes at points (3, 2) and (2, 3) are 16 and 12 respectively, we can set up the following equations:
2A3 + B = 16 2A2 + B = 12
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