Use the process of factoring and completing the square in a quadratic function to show zeros, minimum/maximum values, and symmetry of the graph and interpret these in terms of a context.
Example Problems
Let
Where does p have critical points?
Where does p have critical points?
Determine the vertex of the parabola represented by:
Determine the vertex of the parabola represented by:
Khan Academy ResourcesSolving quadratics by factoring reviewCompleting the square reviewSolving quadratics by factoringQuadratics by factoring (intro)Completing the square (intermediate)Completing the squareQuadratics by factoringSolve equations using structureCompleting the square (intro)Worked example: completing the square (leading coefficient ≠ 1)Completing the squareSolving quadratics by factoringSolving quadratics by completing the square: no solutionFinding the vertex of a parabola in standard formSolving quadratics by factoring: leading coefficient ≠ 1Worked example: Rewriting & solving equations by completing the squareWorked example: Rewriting expressions by completing the square
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