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

Nov 25, 2015

${x}_{\text{vertex}} = 3$ Look at the explanation. I will let you take my stop point on to find ${y}_{\text{vertex}}$

#### Explanation:

$\textcolor{b l u e}{M e t h o d 1}$

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

$\textcolor{b r o w n}{\text{Consider what is inside the brackets}}$
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 $- 6 x$ by $\frac{1}{2}$. So completing the square has already 'done that bit'

$\textcolor{b l u e}{\text{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}}$
$\textcolor{b l u e}{M e t h o d 2}$
Write as: $y = {x}^{2} - 6 x + 3 - 25$

$y = {x}^{2} - 6 x - 22. \ldots \ldots \ldots \ldots \ldots . . \left(1\right)$

Consider the -6 from $- 6 x$

Then:

${x}_{\text{vertex}} = \left(- \frac{1}{2}\right) \times \left(- 6\right) = + 3. \ldots \ldots . \left(2\right)$

Substitute (2) into (1) and resolve for y which is the value of ${y}_{\text{vertex}}$

So you have ${y}_{\text{vertex}} = {\left(3\right)}^{2} - \left(6 \times 3\right) - 22$

I will let you work that one out!

Nov 25, 2015

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

Ans: vertex (3, -25)

#### Explanation:

This is the vertex form of y. Therefor,
$V e r t e x \left(3 , - 25\right)$