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
