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Completion requirements
Tait converts the quadratic function \(f\left( x \right) = 3x^2 - 12x +
5\) into vertex form by completing the square, ending up with \(f\left( x
\right) = 3\left( {x - 2} \right)^2 - 7 \). Verify his solution both
algebraically and using technology.
Because both sides of the table are equal, it appears that Tait did complete the square correctly.
Check using technology.
Because both graphs are the same, the conversion into vertex form was done correctly.
| Expansion and simplification of vertex form |
Standard form
|
| \(\begin{array}{l} f\left( x \right) = 3\left( {x - 2} \right)^2 - 7 \\ f\left( x \right) = 3\left( {x^2 - 4x + 4} \right) - 7 \\ f\left( x \right) = 3x^2 - 12x + 12 - 7 \\ f\left( x \right) = 3x^2 - 12x + 5 \\ \end{array}\) |
\(f\left( x \right) = 3x^2 - 12x + 5\)
|
Because both sides of the table are equal, it appears that Tait did complete the square correctly.
Check using technology.
| For further information about Completing the Square see pp. 180 to 192 of Pre-Calculus 11. |