Question

Which equation, when graphed, has x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, â€"16)? f(x) = â€"(x â€" 2)(x â€" 4) f(x) = â€"(x 2)(x 4) f(x) = â€"2(x â€" 2)(x â€" 4) f(x) = â€"2(x 2)(x 4).

Answer 1

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.

$y=a(x-2)(x-4)$

Where is $a$ number

Substitute 0 for $x$.

$y=a(0-2)(-4)\\y=8a$

We have y-intercept of (0, –16).

$-16=8a\\a=-2$

The equation would be,

$f(x) = -2(x - 2)(x - 4).$

Thus, the correct option is f(x) = –2(x – 2)(x – 4).

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