Question

Write -4x^2-24x-40 in vertex form

Answer 1

Answer: -4(x + 3)^2 + 104

Explanation:

To write -4x^2 - 24x - 40 in vertex form, we need to complete the square. First, let's factor out the common factor of -4:

-4(x^2 + 6x + 10)

Now, let's complete the square inside the parentheses. Take half of the coefficient of x (which is 6), square it (which is 36), and add it inside the parentheses:

-4(x^2 + 6x + 36 - 36 + 10)

Simplifying, we get:

-4((x + 3)^2 - 26)

Now we can distribute the -4:

-4(x + 3)^2 + 104

So, the vertex form of -4x^2 - 24x - 40 is -4(x + 3)^2 + 104.