Answer:
see explanation
Step-by-step explanation:
To find the roots let f(x) = 0, that is
x² - 2x - 3 = 0
(x - 3)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x + 1 = 0 ⇒ x = - 1
Roots are x = - 1, x = 3
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To find the y- intercept let x = 0, that is
f(0) = 0 - 0 - 3 = - 3 ← y- intercept
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The vertex lies on the axis of symmetry which is situated at the midpoint of the roots.
[tex]x_{vertex}[/tex] = [tex]\frac{-1+3}{2}[/tex] = 1
substitute x = 1 into f(x) for y- coordinate of vertex
[tex]y_{vertex}[/tex] = 1² - 2(1) - 3 = 1 - 2 - 3 = - 4
vertex = (1, - 4)
