A function f() is graphed on the coordinate plane.
1 answer:
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Answer:
-3x > -30
Step-by-step explanation:
The graph can be described simply as ...
x < 10
If we multiply the equation by -3, we have to reverse the inequality symbol. Then we get ...
-3x > -30
Quadratic Function
We are given the function
1) Find the zeros of the function
The zeros or roots of f, are found by equating it to 0:
The standard representation of a quadratic function is:
where a,b, and c are constants.
Solving with the quadratic formula:
The coefficients can be established by comparing the generic equation with the given equation, thus: a=1, b=19, c=60. Substituting:
Operating:
The smaller root is -15, the larger root is -4. Answer:
-15
-4
2) The quadratic equation can be also written in vertex form:
Where a is the leading coefficient and (h,k) is the vertex.
To find this form, we need to complete squares as follows.
We need to recall this identity:
Comparing the given function, we can see the first term is t=a, the second term should be 2ab=19t, thus b=19/2
To complete the square, we need to add and subtract b^2 as follows:
Now we apply the identity:
Finally, we add 121/4:
Comparing with the vertex form of the quadratic function:
a=1
Vertex: (19/2,-121/4)