turkey-yks 2016 Q42

turkey-yks · Other · lys1-math Tangents, normals and gradients Determine unknown parameters from tangent conditions

Let a and b be real numbers. In the rectangular coordinate plane, the parabola
$$y = a x ^ { 2 } + b x$$
passes through the point $( 1,2 )$, and the tangent line to the parabola at this point intersects the y-axis at the point $( 0,1 )$.
Accordingly, what is the product $a \cdot b$?
A) - 3
B) - 2
C) - 1
D) 2
E) 4

Let a and b be real numbers. In the rectangular coordinate plane, the parabola

$$y = a x ^ { 2 } + b x$$

passes through the point $( 1,2 )$, and the tangent line to the parabola at this point intersects the y-axis at the point $( 0,1 )$.

Accordingly, what is the product $a \cdot b$?\\
A) - 3\\
B) - 2\\
C) - 1\\
D) 2\\
E) 4

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