Question

What is the vertex of `y=(x-3)^2-25`?

Answer 1

`x_("vertex") = 3` Look at the explanation. I will let you take my stop point on to find `y_("vertex")`

Explanation:

`color(blue)(Method 1)`

What you are given in the question is in the format of 'completing the square'.

`color(brown)("Consider what is inside the brackets")`
The -3 is negative but the answer is +3. So all you have to do is use the number (in this case it is 3) and change its sign.

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Then as in Method 2; substitute for `x` to find `y`
.
In effect; method 1 is the same process as in method 2 it is just that it looks different

For completing the square the -3 in the bracket is obtained by multiplying the -6 in `-6x` by `1/2`. So completing the square has already 'done that bit'

`color(blue)("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")`
`color(blue)(Method 2)`
Write as: `y=x^2 -6x+3-25`

`y=x^2-6x-22..................(1)`

Consider the -6 from `-6x`

Then:

`x_("vertex") = (-1/2)xx(-6)=+3........(2)`

Substitute (2) into (1) and resolve for y which is the value of `y_("vertex")`

So you have `y_("vertex")= (3)^2-(6xx3)-22`

I will let you work that one out!

Answer 2

Find the vertex of y = (x - 3)^2 - 25

Ans: vertex (3, -25)

Explanation:

This is the vertex form of y. Therefor,
`Vertex (3, -25)`