Answer:
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.