Write the function to represent the given graph

1. y = -|x - 3| + 4

1. Step-by-step explanation:

NOTES: Observe the coordinates of the vertex (h, k).  Then count the slope (rise over run) from the vertex toward the right.  Then input the values of a, h, & k a into the equation: y = a|x - h| + k

Vertex (h, k) = (3, 4)   → h = 3, k = 4        

slope from vertex toward the right is 1 unit down & 1 unit right → a = -1

y = a|x - h| + k

y = -|x - 3| + 4

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2.

2. Step-by-step explanation:

Vertex (h, k) = (-4, 0)   → h = -4, k = 0        

slope from vertex toward the right is 1 unit up & 2 units right →

y = a|x - h| + k

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3. y = 2|x - 5| - 2

3. Step-by-step explanation:

Vertex (h, k) = (5, -2)    → h = 5, k = -2    

slope from vertex toward the right is 2 units up & 1 unit right → a = 2

y = a|x - h| + k

y = 2|x - 5| - 2

tell you what. i'll find the length of the medians and you can fill in the blanks where they belong.

br

b = (2a,0)

r = (a/2,b/2) remember these things are medians. they go to the 1/2 way point of the line opposite the vertex they face.

br^2 =   (2a - a/2)^2 + (0 - b/2)^2

br^2 = (3/2 a) ^2 + b^2 / 4

br^2 = 9/4 a^2 + b^2 / 4   we need to find some relationship between a and b.

let's try ab = bc  

ab = 2a

bc = (2a - a)^2 + (b - 0)^2

bc = sqrt(a^2 + b^2)

ab = bc

2a = sqrt(a^2 + b^2) square both sides.

4a^2 = a^2 + b^2 subtract a^2 from both sides.

sqrt(3a^2) = sqrt(b^2)

sqrt(3)a = b

let's put b into br^2

br^2 = 9/4 a^2 + 3b^2 / 4

br^2 = 12 a^2 / 4

br^2 = 3a^2 

br = sqrt(3) * a

cp

c = (a,b) ; p = (a,0) this is another application of the distance formula, and it is a good one.

cp^2 = (a - a)^2 + (b - 0)^2

cp^2 = 0 + b^2

cp^2 = b^2 which you can see from the diagram. 

cp = sqrt(b^2)

cp = b but b = sqrt(3) * a 

cp = sqrt(3)*a

aq

a = (0,0)

q = (3/2) a, b/2

aq^2 = (3a/2 -0)^2 + (b/2 - 0)^2

aq^2 = 9a^2/4 + b^2/4

but b = sqrt(3) * a 

aq^2 = 9a^2 / 4 + (sqrt(3)*a)^2 /4

aq^2 = 9 a^2/ 4 + 3 a^2 / 4

aq^2 = 12 a^2/4

aq^2 = 3 a^2

aq = (sqrt  3) * a which agrees with the other two.