Warm Up


Introduction to Standard Form

Expand and simplify the quadratic function \(f\left( x \right) = -2\left( {x - 4} \right)^2 + 3 \). What do you notice when you compare the two forms?

\(\begin{array}{l}
 f\left( x \right) = - 2\left( {x - 4} \right)^2  + 3 \\
 f\left( x \right) = - 2\left( {x - 4} \right)\left( {x - 4} \right) + 3 \\
 f\left( x \right) = - 2\left( {x^2 - 4x - 4x + 16} \right) + 3 \\
 f\left( x \right) = - 2\left( {x^2 - 8x + 16} \right) + 3 \\
 f\left( x \right) = - 2x^2 + 16x - 32 + 3 \\
 f\left( x \right) = - 2x^2 + 16x - 29 \\
 \end{array}\)


Answers will vary for what you notice. The most obvious, perhaps, is that the leading coefficient, \(a = –2\), is present in both forms.