What is the minimum value of the function f(x) = 4x^2 - 16x + 20? (2021)

What is the minimum value of the function f(x) = 4x^2 - 16x + 20? (2021)

Step 1: Identify the function we need to analyze, which is f(x) = 4x^2 - 16x + 20.
Step 2: Recognize that this is a quadratic function in the form of ax^2 + bx + c, where a = 4, b = -16, and c = 20.
Step 3: Since the coefficient of x^2 (which is 4) is positive, the parabola opens upwards, meaning it has a minimum point.
Step 4: To find the x-coordinate of the vertex (minimum point), use the formula x = -b/(2a). Here, b = -16 and a = 4.
Step 5: Calculate x = -(-16)/(2*4) = 16/8 = 2.
Step 6: Now, substitute x = 2 back into the function to find the minimum value: f(2) = 4(2^2) - 16(2) + 20.
Step 7: Calculate f(2): f(2) = 4(4) - 32 + 20 = 16 - 32 + 20 = 4.
Step 8: Therefore, the minimum value of the function is 4.

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