Question

F(x)=-(x+3)(x+10) pls help

Answer 1

Zeros: x = -10 and x = -3

Vertex:
`(-(13)/(2) , (49)/(4) )`

Explanation:

Pre-Solving

We are given the following function:
f(x) = -(x+3)(x+10)

We want to find the zeros and the vertex of the parabola.

Solving

Zeros

The zeros are the values of the function where f(x) = 0.

So, in order to find the zeros, we can set f(x) = 0.

0 = -(x+3)(x+10)

We can divide both sides by -1, to get:

0 = (x+3)(x+10)

To solve this, we will use zero product property.
Split and solve:

x+3 = 0

x = -3

x+10=0

x = -10

Vertex

Now, to find the vertex, we first get the average of the zeros.

Add the values of the zeros together, then divide by two:

`(-3-10)/(2)` =
`(-13)/(2)`

Now, we plug this in for x to get the y value (found through f(x)) of the vertex.

`f(-(13)/(2)) = -(-(13)/(2) + 3) (-(13)/(2) + 10)` =
`(49)/(9)`

So, the vertex is
`(-(13)/(2) , (49)/(4) )`