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

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