If f(x)= x squared-2x-8 and g(x)= 1/4x-1 for which values of x is f(x)=g(x)? explain and show work a. -1.75 and -1.438 b. -1.75 and 4 c. -1.438 d. 4 and 0

Step-by-step explanation:

ƒ(x) = x² - 2x – 8; g(x) = ¼x -1

If ƒ(x) = g(x), then

x² - 2x – 8 = ¼x -1

One way to solve this problem is by completing the square.

Step 1. Subtract ¼ x from each side

Step 2. Move the constant term to the other side of the equation

Step 3. Complete the square on the left-hand side

Take half the coefficient of x, square it, and add it to each side of the equation.

Step 4. Write the left-hand side as a perfect square

Step 5. Take the square root of each side

Step 6. Solve for x

Check:

The diagram below shows that the graph of g(x) intersects that of the parabola ƒ(x) at x = -1.7 and x = 4.