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# The line $x = k$ intersects the graph of the parabola $x = -2y^2 - 3y + 5$ at exactly one point. What is $k$?

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The line $x = k$ intersects the graph of the parabola $x = -2y^2 - 3y + 5$ at exactly one point. What is $k$?

Jun 21, 2022

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The line $$x = k$$ can only intersect the parabola at the vertex.

The y-coordinate of the vertex is $$-{b \over 2a} = {-3 \over 4}$$

Substituting this in for y gives us: $$x = -2(-0.75)^2 - 3(-0.75) + 5$$, meaning $$k = \color{brown}\boxed{6 {1 \over 8}}$$

Jun 21, 2022