Differentiate y=x^2+bx+c, and hence find b and c if: the parabola has y-intercept and has gradient -2 there?

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Answer 1 · 2018-06-04T00:11:21

# b = -2 #

There is insufficient information to find #c#

We have a Parabola with equation # y = x^2 + bx + c # and tangent gradient #-2# at the #y#-intercept:

Differentiating wrt #x# we get:

# y' = 2x+b #

The tangent has gradient #-2# at the #y#-intercept, thus:

# y'(0) = -2 => 2(0)+b = -2 => b = -2 #

Thus we can write the equation:

# y = x^2 - 2x + c #

There is insufficient information to find #c#