Let f (x) = - 2x^2 and g (x) = 2x - 4. On the set of axes, draw the graphs of y = f (x) and

y = g (x).

Using this graph, determine and state all values of x for which f (x) = g (x).

F (x) = - 2x²

g (x) = 2x - 4

f (x) = g (x)

-2x² = 2x - 4

-2x² - 2x = 2x - 2x - 4

-2x² - 2x + 4 = - 4 + 4

-2x² - 2x + 4 = 0

-2 (x²) - 2 (x) - 2 (-2) = 0

-2 (x² - x - 2) = 0

-2 - 2

x² - x - 2 = 0

x² + 2x - x - 2 = 0

x (x) + x (2) - 1 (x) - 1 (2) = 0

x (x + 2) - 1 (x + 2) = 0

(x - 1) (x + 2) = 0

x - 1 = 0 or x + 2 = 0

+ 1 + 1 - 2 - 2

x = 1 or x = - 2

f (x) = g (x)

-2x² = 2x - 4

-2 (-2) ² = 2 (-2) - 4

-2 (4) = - 4 - 4

-8 = - 8

or

f (x) = g (x)

-2x² = 2x - 4

-2 (1) ² = 2 (1) - 4

-2 = 2 - 4

-2 = - 2

Solution Sets: { (-2, - 8), (1, - 2) }