Answer:
vertex = ( - [tex]\frac{3}{2}[/tex], [tex]\frac{75}{4}[/tex] )
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
Given
y = - 3(x - 1)(x + 4) ← expand the factors using FOIL
= - 3(x² + 3x - 4) ← distribute parenthesis by - 3
= - 3x² - 9x + 12 ← in standard form
with a = - 3 and b = - 9 , thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-9}{-6}[/tex] = - [tex]\frac{3}{2}[/tex]
Substitute this value into the equation for corresponding value of y
y = - 3( - [tex]\frac{3}{2}[/tex] - 1)( - [tex]\frac{3}{2}[/tex] + 4)
= - 3 × - [tex]\frac{5}{2}[/tex] × [tex]\frac{5}{2}[/tex]
= - 3 × - [tex]\frac{25}{4}[/tex]
= [tex]\frac{75}{4}[/tex]
Thus
vertex = ( - [tex]\frac{3}{2}[/tex], [tex]\frac{75}{4}[/tex] )
