Instructions: drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. match the parabolas represented by the equations with their vertices.

(-1.75, -1.125) → y = 2x² + 7x + 5

(-3, -1) → y = x² + 6x + 8

(-4, -4) → y = 2x² + 16x + 28

(2.5, 20.25) → y = -x² + 5x + 14

Step-by-step explanation:

We have to find the vertices of the parabolas given in the picture.

A). y = x² + 6x + 8

We will convert this equation into vertex form as y = (x - h)² + k

then vertex will be (h, k)

y = x² + 6x + 8

y + 1 = x² + 6x + 9

y + 1 = (x + 3)²

y = (x + 3)² - 1

y = [x - (-3)]² + (-1)

So vertex will be (-3, -1)

B). y = 2x² + 16x + 28

y = 2[x² + 8x + 14]

y = 2[x² + 8x + 16 - 2]

y = 2[(x + 4)²- 2]

y = 2[{x -(-4)}² - 2]

y = [2{x-(-4)}²] - 4

Therefore, vertex will be (-4, -4)

C). y = -x² + 5x + 14

y = -[x² - 5x - 14]

y = -[x² - 2(2.5x) - (2.5)²+ (2.5)² - 14]

y = -[(x - 2.5)² - 6.25 - 14]

y = -[(x - 2.5)² - 20.25]

Therefore, vertex will be (-2.5, - 20.25)

D). y = -x² + 7x + 7

y = -[x² - 7x - 7]

y = -[ x² - 2(3.5)x + (3.5)²- (3.5)²- 7]

y = -[(x - 3.5)²-12.25 - 7]

y = -[(x - 3.5)² - 19.5]

Therefore, vertex will be (-3.5, 19.5)

E). y = 2x² + 7x + 5

y = 2[x² + (3.5)x + 2.5]

y = 2[x²+ 2(1.75)x + (1.75)²-(1.75)² + 2.5]

y = 2[(x + 1.75)²- 3.0625 + 2.5]

y = 2[{x + 1.75)² - 0.5625]

y = 2(x + 1.75)² - 1.125

therefore, vertex will be (-1.75, 1.125)

i hope this is what you were looking for.

see attached graph

10 down (bang1)

5 up

5down (2)

2.5 up

2.5 down (3)

1.25 up

1.25 down (4)

now add them up : )

hoped i lol