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# Completing The Square

Learn how to eliminate the linear term and see through messy quadratics. You’ll know just how high to shoot your three-pointer to avoid tall defenders.

# Completing the Square - Find the Vertex

What is the minimum value of the quadratic function $y=2x^2+4x+16?$

The vertex of the parabola $$y=x^2-12x+40$$ is $$P=(a, b)$$. If the $$y$$-intercept is $$Q=(0, c)$$, what is the value of $$a+b+c$$?

If a parabola $$y=ax^2-bx+c$$ has its vertex at point $$(5, -8)$$ and passes through the point $$(1, 8)$$, what is the value of $$a+b+c$$?

For fixed real numbers $$a$$ and $$b$$, the parabola $$y=2x^2-4ax+2a^2-b^2+16b$$ has its vertex on parabola $$y=x^2-8x+80$$. What is the value of $$a+b$$?

Given the parabola $$y=-x^2+8x+1,$$ what is the maximum $$y-$$coordinate over all points on the parabola?

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