Answer:
(2p+9)^2
Step-by-step explanation:
We know this is a perfect square trinomial
a^2 +2ab +b^2 = (a+b)^2
a = 2p b = 9
a^2 = 4p^2
2ab = 2*2p*9 = 36p
b^2 = 81
Check
4p^2 +36p+81 = (2p+9)^2
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Answer:
I assume that this is a quadratic equation, something like:
y = -47*x^2 - 24x + (-36)
we can rewrite it as:
y = -47x^2 - 24x - 36
Ok, this is a quadratic equation and we want to find the maximum value.
First, you can notice that the leading coefficient is negative.
This means that the arms of the graph will open downwards.
Then we can conclude that the vertex of the equation is the "higher" point, thus the maximum value will be at the vertex.
Remember that for a general function
y = a*x^2 + b*x + c
the vertex is at:
x = -b/2a
So, in our case:
y = -47x^2 - 24x - 36
The vertex will be at:
x = -(-24)/(2*-47) = -12/47
So we just need to evaluate the function in this to find the maximum value.
Remember that "evaluating" the function in x = -12/47 means that we need to change al the "x" by the number (-12/47)
y = -47*(-12/47)^2 - 24*(-12/47) - 36
y = -32.94
That is the maximum value of the function, -32.94
Solve x by simplifying both sides of the equation & then isolating the variable x=-4 & the negative comes in from the -12
