Answer:
[tex]\large\boxed{y=-(x+5)^2+5}[/tex]
Step-by-step explanation:
The vertex form of a quadratic equation y = ax² + bx + c :
y = a(x - h)² + k
(h, k) - vertex
We have the equation
[tex]y=-x^2-10x-20[/tex]
Convert to the vertex form:
[tex]y=-x^2-2(x)(5)-20[/tex]
[tex]y=-x^2-2(x)(5)-5^2+5^2-20[/tex]
[tex]y=-(\underbrace{x^2+2(x)(5)+5^2}_{(*)})+25-20[/tex] use (a + b)² = a² - 2ab + b²
[tex]y=-(x+5)^2+5[/tex]
