#### Question

# Algebra 1 help; Give the coordinates of the vertex for the graph.?

These are the only 2 questions of the section that I do not understand / can't figure out.

If you can help would you please show the work? Thanks.

1. y = 2x^2 + 4x

2. y = 3k^2 + 12k +9

Thank you.

#### Answer

ok ill help you.

both of these are quadratic equations. any equations that have a number squared as its highest term (when talking about exponents) are quadratic. i dont know if that makes sense.

well all quadratic equations have an a, b, and c.

quadratic equations are really written like this: y = ax^2 + bx + c

the a: the a is the coefficient of the number squared. in your first equation, it is the 2 before the x.

the b: the b is the coefficient of the second term (usually) which in this case is the 4 before the x.

the c: the c is the last number which does not have an x. its all alone. the one in your first equation is 0! you have none. its just invisible lol. in the second equation it is the 9.

now lets say you have an equation like this: y = x^2 + 4

your a is 1, your b is 0, and your c is 4. get it? your you dont have a b, because you dont have another term with just a number in front of an x. its invisible.

okay now time to help you. if you dont understand any of that up there (you need to in order to understand this next part) then please add details and tell me what you dont get and ill help you out!

in order to find the x coordinate of the vertex of your graph, you need to solve this equation.

x = -b/2a

so for your first equation, a = 2, b = 4, and c = 0.

so substitute:

x = -4/2 * 2

simplify:

x = -4/4

x = -1.

now that you know your x, then you just plug it in into the equation.

y = 2(-1)^2 + 4 * -1

don't be fooled and forget to put a value of x with a negative sign (like -1) in parenthesis when squaring it. otherwise you won't get the right answer!

simplify : y = 2 * 1 + 4 * -1

multiply: y = 2 - 4

subtract: y = -2

so your vertex is (-1, -2). since your A (2) is a positive number, your graph will curve up on both sides. ill show you a picture of what one looks like in case youve never seen one before.

http://www.google.com/imgres?imgurl=http…

woah. lol thats it. so click that and youll see what you're dealing with.

okay on to number 2!

2.) y = 3k^2 + 12k + 9

normally i wouldnt do both problems for someone but this is really a difficult concept so i will.

a = 3, b = 12, c = 9.

x = -b/2a

x = -12/2 * 3

x = -12/6

x = -2

y = 2(-2)^2 + 12 * -2 + 9

y = 2 * 4 + 12 * -2 + 9

y = 8 + 12 * -2 + 9

y = 8 - 24 + 9

y = -7

x = -2, y = -7, so your coordinate? (-2, -7). and since A (3) is positive, it will curve up on both sides.

hope this helped. its actually really diffficult to understand at first and good luck with it :) ill be glad to explain more if youre having problems