Maths-

General

Easy

Question

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

h(x) = x^{2} + x – 3.5

## The correct answer is: -3.75

### We have given two functions f(x) and h(x).

h(x) = x^{2} + x – 3.5

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 h(x) = x^{2} + x – 3.5, a= 1, b= 1, and c = -3.5. So, the equation for the axis of symmetry is given by

x = −(1)/2(1)

x = -1/2

x = -0.5

The equation of the axis of symmetry for h(x) = x^{2} + x – 3.5 is x = -0.5.

The x coordinate of the vertex is the same:

h =-0.5

The y coordinate of the vertex is :

k = f(h)

k = h^{2} + h – 3.5

k = (-0.5)^{2} + (-0.5) – 3.5

k = 0.25 – 0.5 – 3.5

k = -3.75

Therefore, the vertex is (-0.5 , -3.75)

The minimum value of g(x) will be the y-coordinate of vertex = -3.75

The equation of the axis of symmetry for h(x) = x

^{2}+ x – 3.5 is x = -0.5.

The x coordinate of the vertex is the same:

The y coordinate of the vertex is :

^{2}+ h – 3.5

^{2}+ (-0.5) – 3.5

Therefore, the vertex is (-0.5 , -3.75)

The minimum value of g(x) will be the y-coordinate of vertex = -3.75