Question

Which of the following equations is shown graphed?

(The list of answers is one of the pictures below)

Answer 1

y = -
`(1)/(2)` x² - 2x + 6

Explanation:

given zeros x = a and x = b ( where graph crosses the x- axis ) , then the corresponding factors are (x - a) and (x - b)

the equation is then the product of the factors

y = a(x - a)(x - b) ← a is a multiplier

From the graph the zeros are x = - 6 and x = 2 , then the factors are

(x - (- 6) ) and (x - 2) , that is (x + 6)(x - 2) , so

y = a(x + 6)(x - 2) ← expand factors using FOIL

= a(x² + 4x - 12)

to find a , substitute any other point on the graph into the equation

using the y- intercept (0, 6 )

6 = a(0² + 4(0) - 12)

6 = - 12a ( divide both sides by - 12 )

`(6)/(-12)` = a

-
`(1)/(2)` = a , the equation is

y = -
`(1)/(2)` (x² + 4x - 12) ← distribute parenthesis by -
`(1)/(2)`

y = -
`(1)/(2)` x² - 2x + 6