Maths-
General
Easy
Question
What is the maximum value of f(x)= -4x2 +16x+12
The correct answer is: 28
Solution:- We have given a function
f(x) = -4x2 +16x+12
We have to find the maximum value of function
On comparing with the standard form of the function f(x)=ax2+bx+c.
For finding the maximum value of function we have to find the vertex of it.
In f(x)= -4x2 +16x+12, a= -4, b= 16, and c= 12. So, the equation for the axis of symmetry is given by
x = −(16)/2(-4)
x = -16/-8
x = 2
The equation of the axis of symmetry for f(x)= -4x2 +16x+12 is x = 2.
The x coordinate of the vertex is the same:
h = 2
The y coordinate of the vertex is :
k = f(h)
k = -4h2 +16h+12
k = -4(2)2 +16(2)+12
k = -16 + 32 + 12
k = 28
Therefore, the vertex is (2 , 28)
The maximum value of function will be the y-coordinate of vertex = 28
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