Completing The Square

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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