SOLUTION: Find the following for the function f(x)=(x+6)^2 (x-3)^2. a) Find the x- and y- intercepts of the polynomial function f. b) Determine whether the graph of f crosses or touches th

Question 766277: Find the following for the function f(x)=(x+6)^2 (x-3)^2.
a) Find the x- and y- intercepts of the polynomial function f.
b) Determine whether the graph of f crosses or touches the x-axis at each x-intercept.
c)Put all the information together to obtain the graph of f.
The x-intercepts is(are)___________
The y-intercept of f is___________.
Does the graph cross or touch the x-axis at the smaller x-intercept?
a) The graph touches the x-axis.
b) the graph crosses the x-axis.
Does the graph cross or touch the x-axis at the larger x-intercept?
a)the graph touches the x-axis.
b)the graph crosses the x-axis.
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Some limited help...

Two zeros are -6 and +3. This means f(-6)=0 and f(3)=0, so you have x intercepts of (-6,0) and (3,0).

Vertical axis intercept? Try y=(0+6)^2(0-3)^2=36*9=324.
y-intercept is (0,324).

Check sign of f in the three intervals.

f=(-)^2 *(-)^2=(+) positive
In fact, look at this function! Each binomial factor is squared. This function will be positive everywhere. Not necessary to check in the other two intervals.

Because the graph has TWO zeros, and is POSITIVE everywhere, the graph will TOUCH but not cross below the x-axis at (-6,0) and (3,0).

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