What is the end behavior of h(x)=-5x^4+13x/x^3
1 answer:
The end behavior of h(x)= (-5 + 13x ) / x³ is both ends will point in the negative direction.
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
We have h(x)= (-5 + 13x ) / x³
The leading term of this polynomial is -5 (it has the highest degree) where the degree is 4 (even) and the leading coefficient is -5 [it is negative.
Since, this function is even, and the leading coefficient is negative, both ends will point in the negative direction.
Learn more about this concept here:
#SPJ1
You might be interested in
Answer:
Step-by-step explanation:
This is written in the standard form of a quadratic function:
where:
- ax² → quadratic term
- bx → linear term
- c → constant
You need to convert this to vertex form:
where:
- (h,k) → vertex
To find the vertex form, you need to find the vertex. For this, use the equation for axis of symmetry, since this line passes through the vertex:
Using your original equation, identify the a, b, and c terms:
Insert the known values into the equation:
Simplify. Two negatives make a positive:
X is equal to 3 (3,y). Insert the value of x into the standard form equation and solve for y:
Simplify using PEMDAS:
The value of y is -6 (3,-6). Insert these values into the vertex form:
Insert the value of a and simplify:
:Done
Factoring, you have
h(t) = -16(t^2 -2 -8) = -16(t -4)(t +2)
The ball hits the ground when h(t) = 0, so
0 = -16(t -4)(t +2)
t = 4 or -2
The positive solution is the one of interest.
It will take 4 seconds for the ball to hit the ground.
h(t) = -16(t^2 -2 -8) = -16(t -4)(t +2)
The ball hits the ground when h(t) = 0, so
0 = -16(t -4)(t +2)
t = 4 or -2
The positive solution is the one of interest.
It will take 4 seconds for the ball to hit the ground.