Question

The function intersects its midline at（pi, -4）and has a minimum point at (pi/4, -5.5) what is the formula for f(x)?

Answer 1

Answer:

$f(x)=\frac{2}{\pi}(x-\pi)-4$

Step-by-step explanation:

Given: The function intersects its midline at $(\pi,-4)$ and has a minimum point at $(\frac{\pi}{4} ,-5.5)$

To find: function f(x)

Solution:

Equation of a line joining points $(x_1,y_1),(x_2,y_2)$ is given by $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Take $(x_1,y_1)=(\pi,-4)\,,\,(x_2,y_2)=(\frac{\pi}{4} ,-5.5)$

$y+4=\frac{-5.5+4}{\frac{\pi}{4}-\pi }(x-\pi)\\ =\frac{-1.5(4)}{-3\pi}(x-\pi)\\ =\frac{2}{\pi}(x-\pi)$

$f(x)=y=\frac{2}{\pi}(x-\pi) -4$