Question

2. Which equation represents y=-x2 - 10x-20 in vertex form?
y=-(x+5)* + 10
y=-(x– 5)° +15
y=-(x - 5)*+5
y=-(x+5)* +5

Answer 1

Answer:

$\large\boxed{y=-(x+5)^2+5}$

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

$y=-x^2-10x-20$

Convert to the vertex form:

$y=-x^2-2(x)(5)-20$

$y=-x^2-2(x)(5)-5^2+5^2-20$

$y=-(\underbrace{x^2+2(x)(5)+5^2}_{(*)})+25-20$       use (a + b)² = a² - 2ab + b²

$y=-(x+5)^2+5$