Question

State the zero(s) and y-intercept of the following function: f(x) = x(x + 3)

Your answer may be exact or rounded to the nearest hundredth.​

Answer 1

zeros are x = 0 and x = -3

y-intercept is y = 0

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Step-by-step explanation:

y = f(x)

The equation we have is y = x(x+3)

Plug in y = 0 and solve for x to get the x-intercepts, aka roots, aka zeros of a function.

y = x(x+3)

0 = x(x+3)

x(x+3) = 0

x = 0 or x+3 = 0 .... zero product property

x = 0 or x = -3 are the two roots, or zeros

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To find the y-intercept, plug in x = 0 and compute to get the following value:

y = x(x+3)

y = 0*(0+3)

y = 0*3

y = 0 is the y-intercept

In this case, the y-intercept is at the same location as one of the x-intercepts.