Step-by-step explanation:
- move 2.4x to the left-hand side and change its sign.
- move y to the right-hand side and change its sign.
- Divide both sides of the equation by -2.4
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answer:
Step-by-step explanation:
On this question we see that we are given two points on a certain graph that has a maximum point at 57 feet and in 0.76 seconds after it is thrown, we know can say this point is a turning point of a graph of the rock that is thrown as we are told that the function f determines the rocks height above the road (in feet) in terms of the number of seconds t since the rock was thrown therefore this turning point coordinate can be written as (0.76, 57) as we are told the height represents y and x is represented by time in seconds. We are further given another point on the graph where the height is now 0 feet on the road then at this point its after 3.15 seconds in which the rock is thrown in therefore this coordinate is (3.15,0).
now we know if a rock is thrown it moves in a shape of a parabola which we see this equation is quadratic. Now we will use the turning point equation for a quadratic equation to get a equation for the height which the format is , where (p,q) is the turning point. now we substitute the turning point
, now we will substitute the other point on the graph or on the function that we found which is (3.15, 0) then solve for a.
0 = a(3.15 - 0.76)^2 + 57
-57 =a(2.39)^2
-57 = a(5.7121)
-57/5.7121 =a
-9.9788169 = a then we substitute a to get the quadratic equation therefore f is
ANSWER
The restrictions are
EXPLANATION
We were given the rational function,
The function is defined for all values of a, except
This has become a quadratic trinomial, so we need to split the middle term.
We do that by multiplying the coefficient of which is 5 by the constant term which is 3. This gives us 15.
The factors of 15 that adds up to 16 are 1 and 15.
We use these factors to split the middle term.
We now factor to get,
We factor further to get,
This implies that,
This gives
These are the restrictions.