E
Given a quadratic 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]
y = 10x² + 5x - 7 is in standard form
with a = 10, b = 5 and c = - 7, hence
[tex]x_{vertex}[/tex] = - [tex]\frac{5}{20}[/tex] = - [tex]\frac{1}{4}[/tex]
Substitute this value into the equation for y-coordinate
y = 10 (- [tex]\frac{1}{4}[/tex])² + 5 (- [tex]\frac{1}{4}[/tex]) - 7
= [tex]\frac{5}{8}[/tex] - [tex]\frac{5}{4}[/tex] - 7
= [tex]\frac{5}{8}[/tex] - [tex]\frac{10}{8}[/tex] - [tex]\frac{56}{8}[/tex] = - [tex]\frac{61}{8}[/tex]
vertex = (- 0.25, - 7.625 ) → E
