f(x) = - 2(x - [tex]\frac{1}{4}[/tex])² - [tex]\frac{15}{8}[/tex]
the equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
• the coefficient of the x² term must be 1 , factor out - 2
= - 2(x² - [tex]\frac{1}{2}[/tex]x) - 2
• add / subtract (half the coefficient of the x-term )² to x² - [tex]\frac{1}{2}[/tex]x
= - 2(x² + 2(- [tex]\frac{1}{4}[/tex])x + [tex]\frac{1}{16}[/tex] - [tex]\frac{1}{16}[/tex]) - 2
= - 2(x - [tex]\frac{1}{4}[/tex])² + [tex]\frac{1}{8}[/tex] - 2
= - 2(x - [tex]\frac{1}{4}[/tex])² - [tex]\frac{15}{8}[/tex]
