Question

Suppose the tangent to the parabola $y=x^2+px+q$ at $(0,3)$ has slope $-1$. Then $p+q$ equals.

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is C $2$

$y=x^2+px+q\text{has tangent at (0,3) with slope -1}$

Clearly, (0,3) must lie on the parabola.

Substituting (0,3) in the parabola equation we get

$q=3$

We can get tangent slope by differentiating parabola equation with respect to x

$⟹y^{\prime }=2x+p=-1\text{for point (0,3)}$

$⟹p=-1$

Thus $p+q=2$