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:

2A*3 + B = 16
2A*2 + B = 12

This is a system of linear equations. We can solve it by subtracting the second equation from the first to eliminate B:

2A*3 - 2A*2 = 16 - 12
2A = 4
A = 4/2 = 2

So, the value of A is 2.

Question

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:

2A*3 + B = 16
2A*2 + B = 12

This is a system of linear equations. We can solve it by subtracting the second equation from the first to eliminate B:

2A*3 - 2A*2 = 16 - 12
2A = 4
A = 4/2 = 2

So, the value of A is 2.

Knowee AI · Accepted Answer

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:

2A*3 + B = 16
2A*2 + B = 12

This is a system of linear equations. We can solve it by subtracting the second equation from the first to eliminate B:

2A*3 - 2A*2 = 16 - 12
2A = 4
A = 4/2 = 2

So, the value of A is 2.

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.