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

Answer:

(-5,-28)

Step-by-step explanation:

Look at graph.

Hope this helps!

Answer 2

Answer:

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

Step-by-step 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.