y = (x - 3 )^2 +4 please help solve by identify the minimum or maximum y value

Question

whpalmer4 · Answer

That's a parabola.  If you multiply it out, you'll see that the coefficient on the $x^2$ term is positive, which means the parabola opens up (looks like a bowl).  That means the vertex is the minimum point.  You conveniently have the formula in what is called vertex form:
$$y =a (x-h)^2+k$$ where the vertex is at $(h,k)$.

$a = 1$ in this case.  Where is the vertex?

whpalmer4 · Answer

If you had the formula in expanded or standard form:
$$y = ax^2+bx+c$$you can find the x coordinate of the vertex by 
$$x = -\frac{b}{2a}$$and plug that value of $x$ into the formula to find the y coordinate of the vertex.  Don't need to know that to do this problem, but it beats factoring to get vertex form if you don't already have it.

anonymous · Answer

I am not sure

lncognlto · Answer

The x^2 value is always going to be positive, as the parabola opens upwards and thus will have a minimum value, so it would need to equal 0 for the minimum y value.

whpalmer4 · Answer

Compare your equation with mine:

$$y = (x-3)^2+4$$$$y=(x-h)^2+k$$

what are the values of $h$ and $k$?

anonymous · Answer

please give me a moment to write out

whpalmer4 · Answer

sure, I'm not going anywhere...

anonymous · Answer

I don't know I am having a hard time figuring out algebra

anonymous · Answer

I have a tutor that sits with me once a week an I just can seem to grab on to algebra

anonymous · Answer

are you there?

whpalmer4 · Answer

yes, just got back.

whpalmer4 · Answer

$$y=(x-h)^2+k$$$$y=(x-3)^2+4$$
Look at the corresponding spots in each equation.  Let's find the value of $k$ first.  There are 3 "chunks" in the second equation:
$$y$$$$(x-3)^2$$$$4$$

which of those most resembles $k$ in the first equation?

$4$, right?

anonymous · Answer

yes

whpalmer4 · Answer

Okay, now let's find $h$.  Any ideas?

anonymous · Answer

h would be 3 right?

whpalmer4 · Answer

yes!  (sorry about the delay, my family is bugging me for help on other projects)

anonymous · Answer

understand

whpalmer4 · Answer

So our vertex is at $(h,k)$ and as we found that $h = 3, k = 4$, that means the vertex is at $(3,4)$

whpalmer4 · Answer

There's a nice page talking about parabolas and their formulas here: http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php

anonymous · Answer

okay thank you