Question

I am so confused, please help me! (I know HOW to write the equations, but just not when the info is given to me like this :'( )

Answer 1

Vertex form: \(y=a(x-h)^2+k\), where (h, k) is the vertex.
Looking at the info they gave you, can you tell what either coordinate for the vertex is?

Answer 2

(-2, ? ) im sorry this is a new concept for me

Answer 3

no problem.
The axis of symmetry gives the x-coordinate of the vertex.
The maximum (or minimum when you get a problem like that) height gives the y-coordinate.
So the vertex is (2, 2)

Answer 4

Put that into the equation to get
\(y = a(x -2)^2+2\)

Answer 5

make sense so far?

Answer 6

because it is maximum, wont that make it a negative cooridinate or does that not apply here?

Answer 7

no. The negative doesn't come into play here. Just take the number as they give it to you. The negative comes in as a check. Since it's a maximum \(a\) is supposed to be negative. But you have to plug in the point (3, 0) to find it.

Answer 8

okay, i dont know how to plug in the points in runs through, im not really sure about that part

Answer 9

and yes, i was looking at my chart wrong, i see now that the a is whats supposed to be negative

Answer 10

You have
\(y=a(x-2)^2+2\)
You have to plug in 3 for x and 0 for y, then solve for a.
\[0=a(3-2)^2+2\]

Answer 11

a is our maximum value which is 2, but its negative? so -2?

Answer 12

a is not the maximum value. The y-coordinate of the vertex is the maximum value.

Answer 13

ohhh ok, my bad

Answer 14

so the final answer is \[y=2(x-2)^2-2\]

Answer 15

so how does a=2 ?