Answer: To find the minimum or maximum value of a quadratic function in the form of f(x) = ax^2 + bx + c, we need to use the formula:
x = -b/2a
where the value of x gives us the x-coordinate of the vertex. If a is positive, the vertex represents the minimum value of the function, and if a is negative, the vertex represents the maximum value of the function.
In this case, the given quadratic function is f(x) = x^2 - 8x + 3. We can see that a = 1, b = -8, and c = 3.
Using the formula x = -b/2a, we get:
x = -(-8)/2(1) = 4
So the x-coordinate of the vertex is 4. To find the corresponding y-coordinate, we can substitute x = 4 into the function:
f(4) = 4^2 - 8(4) + 3 = -13
Therefore, the vertex of the function is (4, -13). Since a = 1 is positive, the vertex represents the minimum value of the function.
So the minimum value of the function is -13.
To find the maximum value of the function, we can simply look at the end behavior of the quadratic function. Since a = 1 is positive, the parabola opens upward and there is no maximum value.
Therefore, the minimum value of the function is -13, and there is no maximum value.
Explanation: