# CONVERTING FROM STANDARD FORM TO FACTORED FORM WORKSHEET

Convert the following quadratic function from standard form to factored form.

Problem 1 :

y = x2 - 4x + 4

Solution

Problem 2 :

y = 2x2 - x - 1

Solution

Problem 3 :

y = x2 - 5x + 6

Solution

Problem 4 :

y = x2 - 5x - 6

Solution

Problem 5 :

y = x2 - 17x + 72

Solution

Problem 6 :

y = 4x2 - 12x + 9

Solution

Problem 7 :

y = 4x2 + 28x + 49

Solution

Problem 8 :

y = 9x2 + 6x + 1

Solution

1)  y = (x - 2) (x - 2)

2)  y = (2x + 1) (x - 1)

3)  y = (x - 2) (x - 3)

4)  y = (x - 6) (x + 1)

5)  y = (x - 8) (x - 9)

6)  y = (2x - 3) (2x - 3)

7)  y = (2x + 7) (2x + 7)

8)  y = (3x + 1) (3x + 1)

Problem 1 :

Convert f(x) = 3x2 + 18x - 48 to factored form.

Solution

Problem 2 :

Factorize 2x2 +4x + 2

Solution

Problem 3 :

The height of the foot ball kicked from the ground is given by the function h(t) = -5t2 + 20, where h(t) is height in meters and t is the time in seconds from its release.

(i)  Write the function in factored form.

(ii)  When will the foot ball hit the ground ?

Solution

Problem 4 :

Solve x2 - 8x + 12 = -3

Move everything to one side and find zeros.

Solution

Problem 5 :

Find the points of intersections of the graphs

f(x) = x2 - 8x + 12 and g(x) = -3

Solution

Problem 6 :

The path a dolphin travels when it rises above the ocean’s surface can be modelled by the function

h(d) = -0.2d2 + 2d

where h(d) is the height of the dolphin above the water’s surface and d is the horizontal distance from the point where the dolphin broke the water’s surface, both in feet. When will the dolphin reach a height of 1.8 feet?

Solution

1)  f(x) = 3(x - 2) (x + 8)

2)  f(x) = 2 (x + 1) (x + 1)

3)  i)  h(t) = -5(t + 2) (t - 2)

ii)  t = -2 and t = 2

4)  x = 5 and x = 3

5)  points of intersections are (5, -3) and (3, -3).

6) at d = 1 and d = 9 the dolphin will reach the height 200 m.

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