Answer:
vertex = ([tex]\frac{20}{7}[/tex], - [tex]\frac{225}{7}[/tex] )
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
7n² - 40n + 25 = 0 ← is in standard form
with a = 7, b= - 40 , thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-40}{14}[/tex] = [tex]\frac{20}{7}[/tex]
Substitute this value into the equation for corresponding y- coordinate
7([tex]\frac{20}{7}[/tex] )² - 40([tex]\frac{20}{7}[/tex] ) + 25
= 7([tex]\frac{400}{49}[/tex] ) - [tex]\frac{800}{7}[/tex] + 25
= [tex]\frac{400}{7}[/tex] - [tex]\frac{800}{7}[/tex] + 25
= - [tex]\frac{400}{7}[/tex] + [tex]\frac{175}{7}[/tex] = - [tex]\frac{225}{7}[/tex]
vertex = ( [tex]\frac{20}{7}[/tex], - [tex]\frac{225}{7}[/tex] )
