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

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

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`