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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.
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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 \(a+b+c\)?
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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 \(a+b+c\)?
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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 \(a+b\)?
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Given the parabola \(y=-x^2+8x+1,\) what is the maximum \(y-\)coordinate over all points on the parabola?
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