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)

75

step-by-step explanation:

answer: yard ramps with a level off platform are typically 36 feet long. truck, rather than at an angle, enabling access to those pallets at the very back of the truck. if you are using your yard ramp to convert a loading dock into a drive-in door, we even at 60 inches (5 feet) high and a 30 foot ramp, the slope of the ramp will be less

step-by-step explanation: