Use the intercepts and extreme value to find an equation for the quadratic function. a) f(x) = 2x2 - 3x - 6 b) f(x) = 3x2 - 4x - 6 c) f(x) = 2x2 - 4x - 6 d) f(x) = 2x2 - 4x + 6

C

the x-intercepts are x = -1, x = 3

hence the factors are (x + 1 ) and (x - 3 )

the function is the product of it's factors

f(x) = a(x + 1)(x - 3) ← a is a multiplier

to find a substitute the point (0, - 6 ) from the graph into the equation

- 6 = a(1)(- 3)

- 6 = - 3a ( divide both sides by - 3 )

a = 2

f(x) = 2(x + 1)(x - 3) = 2(x² - 2x - 3 ) = 2x² - 4x - 6 → C

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