Answer:
see explanation
Step-by-step explanation:
The equation of a parabola 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 firm use the method of completing the square
Factor out - 1 from each term
y = - (x² - 9x + 12)[tex]\frac{33}{4}[/tex]
To complete the square
add/subtract (half the coefficient of the x- term )² to x² - 9x
y = - (x² + 2( - [tex]\frac{9}{2}[/tex])x + [tex]\frac{81}{4}[/tex] - [tex]\frac{81}{4}[/tex] + 12 )
= - ( (x - [tex]\frac{9}{2}[/tex])² - [tex]\frac{33}{4}[/tex] )
y = - (x - [tex]\frac{9}{2}[/tex] )² + [tex]\frac{33}{4}[/tex] ← in vertex form
