Question

PLEASE HELP ASAP!!
A function is shown where b is a real number.
f(x) = x^2 + bx + 144
The minimum value of the function is 80.
Create an equation for an equivalent function in the form f(x) = (x - h)^2 + k

Answer 1

$f(x) = {(x + \frac{b}{2})}^{2} + \frac{24 - b}{2}$

Answer 2

The value of b = 16, -16 and the function in the form f(x) = (x - h)² + k is f(x) = (x - 8)² + 80 or f(x) = (x + 8)² + 80

What is a parabola?

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have a parabolic function:

f(x) = x² + bx + 144

The minimum value of the function is 80.

f'(x) = 2x + b = 0

x = -b/2

f''(x) > 2

f(-b/2) = (-b/2)² + b(-b/2) + 144 = 80

b = 16, -16

f(x) = x²-16x+144

or

f(x) = x²+16x+144

f(x) = (x - 8)² + 80

or

f(x) = (x + 8)² + 80

Thus, the value of b = 16, -16 and the function in the form f(x) = (x - h)² + k is f(x) = (x - 8)² + 80 or f(x) = (x + 8)² + 80

Learn more about the parabola here:

brainly.com/question/8708520

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