Question

What are the coordinates of the vertex of the function f(x)=x2+10x−3? (–5, –28) (–5, 28) (5, –28) (5, 28)

Answer 1

(-5,-28)

Explanation:

Look at graph.

Hope this helps!

Answer 2

Option 1 - The vertex of the function is (h,k)=(-5,-28).

Explanation:

Given : Function
`f(x)=x^2+10x-3`

To find : What are the coordinates of the vertex of the function?

Solution :

We have to convert the quadratic function
`y=ax^2+bx+c` into vertex form
`y=a(x-h)^2+k` where (h,k) are the vertex.

Function
`f(x)=x^2+10x-3`

Applying completing the square i.e. add and subtract half square of b,

`f(x)=x^2+10x+5^2-5^2-3`

`f(x)=(x+5)^2-25-3`

`f(x)=(x+5)^2-28`

On comparing with vertex form,

h=-5 and k=-28

So, The vertex of the function is (h,k)=(-5,-28).

Therefore, Option 1 is correct.