Question

what is h(x) = 7 10x x2 written in vertex form? h(x) = (x – 25)2 – 18 h(x) = (x – 5)2 32 h(x) = (x 5)2 – 18 h(x) = (x 25)2 32

Answer 1

Hello,

Answer C

I give you some sign "+".
You will use them later
++++++++++++++++++++++++++++
h(x)=x²+10x+7=x²+2*5x+25-18=(x+5)²-18

Answer 2

option (c) is correct.

The vertex form of given function
`h(x)=7+10x+x^2` is
`h(x)=(x+5)^2-18`

Explanation:

Given :
`h(x)=7+10x+x^2`

We have to write h(x) in vertex form

For a given quadratic function
`f(x)=ax^2+bx+c` the vertex form can be written by completing square in such a way that we get, the equation in the form of
`f(x)=a(x-h)^2+k` , where (h,k) is the vertex.

Consider the given function
`h(x)=7+10x+x^2`

first writing in standard form , we get,

`h(x)=x^2+10x+7`

Using identity,
`(a+b)^2=a^2+b^2+2ab` , we have

x = a , and 2ab = 10x

Comparing , we get, b= 5

we need to add
`b^2` term

So add and subtract 25 in the given function , we get,

`h(x)=x^2+10x+25-25+7`

Simplify , we get,

`h(x)=(x+5)^2-18`

Thus, the vertex form of given function
`h(x)=7+10x+x^2` is
`h(x)=(x+5)^2-18`

option (c) is correct.