Completing The Square

Completing the Square - Find the Vertex


What is the minimum value of the quadratic function y=2x2+4x+16?y=2x^2+4x+16?

The vertex of the parabola y=x212x+40y=x^2-12x+40 is P=(a,b)P=(a, b). If the yy-intercept is Q=(0,c)Q=(0, c), what is the value of a+b+ca+b+c?

If a parabola y=ax2bx+cy=ax^2-bx+c has its vertex at point (5,8)(5, -8) and passes through the point (1,8)(1, 8), what is the value of a+b+ca+b+c?

For fixed real numbers aa and bb, the parabola y=2x24ax+2a2b2+16by=2x^2-4ax+2a^2-b^2+16b has its vertex on parabola y=x28x+80y=x^2-8x+80. What is the value of a+ba+b?

Given the parabola y=x2+8x+1,y=-x^2+8x+1, what is the maximum yy-coordinate over all points on the parabola?


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