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1 answer:
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Answer:
The vertex of the function is at (1,-25)
Step-by-step explanation:
I think your question missed key information, allow me to add in and hope it will fit the orginal one.
<em>Part of the graph of the function f(x) = (x + 4)(x-6) is shown below. </em>
<em>Which statements about the function are true? Select two </em>
<em>options. </em>
<em>The vertex of the function is at (1,-25). </em>
<em>The vertex of the function is at (1,-24). </em>
<em>The graph is increasing only on the interval -4< x < 6. </em>
<em>The graph is positive only on one interval, where x <-4. </em>
<em>The graph is negative on the entire interval </em>
My answer:
Given the factored form of the function:
f(x) = (x + 4)(x-6)
<=> f(x) =
We will convert to vertex form
<=> f(x) = () - 25
<=> f(x) =
=> the vertex of the function is: (1,-25)
We choose: a. The vertex of the function is at (1,-25)
Let analyse other possible answers:
<u>c. The graph is increasing only on the interval -4< x < 6.</u>
Because the parameter a =1 so the graph open up all over its domain and the vertex is the lowest point.
So the graph is increasing in the domain (1, +∞)
=> C is wrong
<u>d. The graph is positive only on one interval, where x <-4</u>
Wrong, The graph is positive only on one interval, where x > 6
<u>e. The graph is negative on the entire interval</u>
Wrong, The graph is negative only on one interval, where -4< x < 6.
In each case, you can start by taking the antilog.
21. x = 4^(3/2)
x = 8
22. 81 = x^(4/3)
81^(3/4) = x = 27
24. 2x - 3 = 6^0
2x = 4 . . . . . add 3
x = 2
25. 5 - x = 16^(1/2)
5 - 4 = x = 1
_____
You're using the relationship of logarithms:
21. x = 4^(3/2)
x = 8
22. 81 = x^(4/3)
81^(3/4) = x = 27
24. 2x - 3 = 6^0
2x = 4 . . . . . add 3
x = 2
25. 5 - x = 16^(1/2)
5 - 4 = x = 1
_____
You're using the relationship of logarithms: