Maths-

General

Easy

Question

# Compare each function to f, shown in the table. Which function has lesser minimum value? Explain

g(x) = 2x^{2} + 8x + 3

## The correct answer is: -5

### Solution:- We have given two functions f(x) and g(x).

g(x) = 2x^{2} + 8x + 3

For f(x) , minimum value of the function will be the y-coordinate of the given point which has minimum values

(1,0) , (2,-3) , (3,-4) , (4,-3) (5,0)

In the given points minimum value of is (3,-4)

So, the ,minimum value of f(x) is -4.

In g(x)= 2x^{2} + 8x + 3, a= 2, b= 8, and c=3. So, the equation for the axis of symmetry is given by

x = −(8)/2(2)

x = -8/4

x = -2

The equation of the axis of symmetry for g(x)= 2x^{2} + 8x + 3 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 = 2h^{2} + 8h + 3

k = 2(-2)^{2} + 8(-2) + 3

k = 8 - 16 + 3

k = -5

Therefore, the vertex is (-2 , -5)

The minimum value of g(x) will be the y-coordinate of vertex = -5

The equation of the axis of symmetry for g(x)= 2x

^{2}+ 8x + 3 is x = -2.

The x coordinate of the vertex is the same:

The y coordinate of the vertex is :

^{2}+ 8h + 3

^{2}+ 8(-2) + 3

Therefore, the vertex is (-2 , -5)

The minimum value of g(x) will be the y-coordinate of vertex = -5

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