3. Elizabeth is designing a ramp and a platform made of wood. Her sketch of the design
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.
Answer: Hello there!
if we define the y-axis as north and the x-axis as east, then we could use vectors (x,y) to represent the locations, where the (0,0) point is the visitors center.
The waterfall is in 6 miles east and 3 miles north of the (0,0), then we could represent it as (6,3)
the picnic site is 1 mile east and 2 miles north of the (0,0) then we could represent it as (1,2)
now we want to calculate the distance between these two points, first, we need to calculate the difference; this is:
(6,3) -(1,2) = (6 -1, 3-2) = (5,1)
if we want to calculate the total magnitude ( which is the total distance) of this vector, we need to use the Pythagorean theorem, where we considere the values of x and y as the cathetus of a triangle rectangle, and we want to obtain the hipotenuse of such triangle:
that we could round up to 5.1 miles, then the correct answer is the d.