Question

Does the function f(x) = 2x^2− 6x + 9 have a minimum or a maximum? Identify its value.

Answer 1

Answer:

minimum value of function is   $\frac{45}{8}$ .

Step-by-step explanation:

Given function represents a parabola.

Now, here coefficient of $x^{2}$ is positive , so the parabola will be facing upwards and thus the function will be having a minimum.

Now, as we know that minimum value of a parabolic function occurs at

x = $\frac{-b}{4a}$ .

Where , b represents the coefficient of x and a represents the coefficient of $x^{2}$ .

here, a = 2 , b = -6

Thus $\frac{-b}{4a}$ = $\frac{6}{8}$

                                            =  $\frac{3}{4}$

So, at x =  $\frac{3}{4}$  minimum value will occur and which equals

y = 2×$\frac{9}{16}$ - $\frac{18}{4}$ + 9 =  $\frac{45}{8}$ .

Thus , minimum value of function is   $\frac{45}{8}$ .