Maths-

General

Easy

Question

# What is the maximum value of f(x)= -4x^{2} +16x+12

## The correct answer is: 28

### Solution:- We have given a function

f(x) = -4x^{2} +16x+12

We have to find the maximum value of function

On comparing with the standard form of the function f(x)=ax^{2}+bx+c.

For finding the maximum value of function we have to find the vertex of it.

In f(x)= -4x^{2} +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)= -4x^{2} +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 = -4h^{2} +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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