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If the slope of parabola = 2 + + y=ax 2 +bx+c, where , , ∈ a,b,c∈ R \ { 0 } {0} at points ( 3 , 2 ) (3,2) and ( 2 , 3 ) (2,3) are 37 37 and 20 20 respectively, then find the value of a

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If the slope of parabola = 2 + + y=ax 2 +bx+c, where , , ∈ a,b,c∈ R \ { 0 } {0} at points ( 3 , 2 ) (3,2) and ( 2 , 3 ) (2,3) are 37 37 and 20 20 respectively, then find the value of a

answers

We can find the slope of the parabola at a point (x, y) by finding the derivative of the equation y = a * x ^ 2 + bx + c

The derivative of y = a * x ^ 2 + bx + c with respect to x is 2ax + b

So, at the point (3, 2), the slope is 2a^ * 3 + b = 34 .

At the point (2, 3), the slope is 2a^ * 2 + b = 12 .

We can use these two equations to solve for a and b:

2a^ * 3 + b = 34

2a^ * 2 + b = 12

Subtracting the second equation from the first, we get:

2a = 22

Therefore, a = 11

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