Question

Determine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value of the function.

Answer 1

Answer:

The function has a minimum value

The minimum value of the function is -4

Step-by-step explanation:

* Lets explain some facts about the quadratic function

- The general form of the quadratic function is f(x) = ax² + bx + c

  where a , b , c are constant

- The quadratic function represented graphically by a parabola

- The parabola is open upward if a is a positive number

- The parabola is open downward if a is a negative number

- If the parabola open upward its vertex point is minimum point and

 the minimum value of the function is the y-coordinate of the

 vertex point

- If the parabola open downward its vertex point is maximum point

 and the maximum value of the function is the y-coordinate of the

 vertex point

- The x-coordinate of the vertex point is (-b/2a)

- The y-coordinates of the vertex point is f(-b/2a)

* Lets solve the problem

∵ f(x) = x² - 6x + 5

∵ f(x) = ax² + bx + c

∴ a = 1 , b = -6 , c = 5

∵ a is a positive value

∴ The function has minimum point

* The function has a minimum value

∵ the minimum value is the y-coordinate of the vertex point

- Lets find the vertex point

∵ The x-coordinate of the vertex point = -b/2a

∴ The x-coordinate of the vertex point = -(-6)/2(1) = 6/2 = 3

- To find the y-coordinate of the vertex point substitute x in the

  function by the x-coordinate of the vertex point

∵ The y-coordinate of the vertex point = f(3)

∴ The y-coordinate of the vertex point = (3)² - 6(3) + 5

∴ The y-coordinate of the vertex point = 9 - 18 + 5 = -4

∴ The minimum value of the function = -4

* The minimum value of the function is -4