Question

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 please A. -1.75 and -1.438 B. -1.75 and 4 C. -1.438 D. 4 and 0 ​

Answer 1

B. -1.75 and 4

Explanation:

f(x)=g(x)

Input the equations

x²-2x-8 = 1/4x-1

add 1 to both sides

and subtract 1/4x from both sides

x²-2 1/4x - 7 = 0

factor

a + b = -2 1/4

a * b = -7

1.75 + -4 = -2 1/4

1.75 * -4 = -7

reverse their symbols

1.75 becomes -1.75 and -4 becomes 4.

Answer 2

`\boxed{\text{B. x = 4 and x = -1.75}}`

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

`x^(2) - (9)/(4)x - 8 = -1`

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

`x^(2) - (9)/(4)x = 7`

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.

`(1)/(2) * (9)/(4) = (9)/(8);\qquad \left((9)/(8)\right)^(2) = (81)/(64)\\\\x^(2) - (9)/(4)x + (81)/(64) = 7(81)/(64) = (529)/(64)`

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

`(1)/(2) * (9)/(4) = (9)/(8);\qquad \left((9)/(8)\right)^(2) = (81)/(64)\\\\x^(2) - (9)/(4)x + (81)/(64) = 7(81)/(64) = (529)/(64)`

Step 5. Take the square root of each side

`x - (9)/(8) = \pm\sqrt{(529)/(64)} = \pm(23)/(8)`

Step 6. Solve for x

`\begin{array}{rlcrl}x - (9)/(8) & =(23)/(8)& \qquad & x - (9)/(8) & = -(23)/(8) \\\\x & =(23)/(8) + (9)/(8)&\qquad & x & = -(23)/(8) + (9)/(8) \\\\x& =(32)/(8) &\qquad & x & \ -(14)/(8) \\\\x& =4 & \qquad & x & -1.75 \\\end{array}\\\\\text{f(x) = g(x) when \boxed{\textbf{x = 4 or x = -1.75}}}`

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.