To find the equation, for the x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, –16) we have to find the nature of the curve.
The correct option is f(x) = –2(x – 2)(x – 4).
Given:
The x-intercepts at (2, 0) and (4, 0).
The y-intercept of (0, –16).
The nature of the graph is quadratic curve. Write the general equation for x-intercept.
[tex]y=a(x-2)(x-4)[/tex]
Where is [tex]a[/tex] number
Substitute 0 for [tex]x[/tex].
[tex]y=a(0-2)(-4)\\y=8a[/tex]
We have y-intercept of (0, –16).
[tex]-16=8a\\a=-2[/tex]
The equation would be,
[tex]f(x) = -2(x - 2)(x - 4).[/tex]
Thus, the correct option is f(x) = –2(x – 2)(x – 4).
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