Math
posted by Untamed on .
Find the Zeros of the following functions
f(x) = x/3 +5
^ That one is layed out so differently I don't understand how to solve.
In each of the following, determine the zeros of the function and determine the yintercept of the graph of the function.
f(x) = 5x^2  35x
f(x) = 3x(x^249)

It's not so different. It just has a fraction. You can always use y instead of f(x)
y = x/3 + 5
To solve, set y=0 and solve for x
0 = x/3 + 5
x/3 = 5
x = 3/5
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The yintercept is always easy. Just plug in x=0 and evaluate y
y = 5x^2  35x
y(0) = 0 so the yintercept is (0,0)
5x^2  35x
= 5x(x7)
so, y=0 when
5x(x7) = 0
x=0 or x=7
The xintercepts are (0,0) and (7,0)
Note that (0,0) is both an xintercept and a yintercept.
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y = 3x(x^2  49)
Think back to your factoring exercises, and recall the difference of two squares:
(a+b)(ab) = a^2  b^2
y = 3x(x+7)(x7)
So, the yintercept is (0,0)
xintercepts are (0,0) (7,0) and (7,0)