if f(x)= x squared2x8 and g(x)= 1/4x1 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
Question
2 Answer

1. User Answers ToastedMiso
Answer:
B. 1.75 and 4
Stepbystep explanation:
f(x)=g(x)
Input the equations
x²2x8 = 1/4x1
add 1 to both sides
and subtract 1/4x from both sides
x²2 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.

2. User Answers znk
Answer:
[tex]\boxed{\text{B. x = 4 and x = 1.75}}[/tex]
Stepbystep 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
[tex]x^{2}  \dfrac{9}{4}x  8 = 1[/tex]
Step 2. Move the constant term to the other side of the equation
[tex]x^{2}  \dfrac{9}{4}x = 7[/tex]
Step 3. Complete the square on the lefthand side
Take half the coefficient of x, square it, and add it to each side of the equation.
[tex]\dfrac{1}{2} \times \dfrac{9}{4} = \dfrac{9}{8};\qquad \left(\dfrac{9}{8}\right)^{2} = \dfrac{81}{64}\\\\x^{2}  \dfrac{9}{4}x + \dfrac{81}{64} = 7\dfrac{81}{64} = \dfrac{529}{64}[/tex]
Step 4. Write the lefthand side as a perfect square
[tex]\dfrac{1}{2} \times \dfrac{9}{4} = \dfrac{9}{8};\qquad \left(\dfrac{9}{8}\right)^{2} = \dfrac{81}{64}\\\\x^{2}  \dfrac{9}{4}x + \dfrac{81}{64} = 7\dfrac{81}{64} = \dfrac{529}{64}[/tex]
Step 5. Take the square root of each side
[tex]x  \dfrac{9}{8} = \pm\sqrt{\dfrac{529}{64}} = \pm\dfrac{23}{8}[/tex]
Step 6. Solve for x
[tex]\begin{array}{rlcrl}x  \dfrac{9}{8} & =\dfrac{23}{8}& \qquad & x  \dfrac{9}{8} & = \dfrac{23}{8} \\\\x & =\dfrac{23}{8} + \dfrac{9}{8}&\qquad & x & = \dfrac{23}{8} + \dfrac{9}{8} \\\\x& =\dfrac{32}{8} &\qquad & x & \ \dfrac{14}{8} \\\\x& =4 & \qquad & x & 1.75 \\\end{array}\\\\\text{f(x) = g(x) when \boxed{\textbf{x = 4 or x = 1.75}}}[/tex]
Check:
[tex]\begin{array}{rlcrl}4^{2}  2(4)  8 & = \dfrac{1}{4}(4) 1&\qquad & (1.75)^{2}  2(1.75)  8 & = \dfrac{1}{4}(1.75)  1\\\\16  8 8& = 1  1&\qquad & 3.0625 +3.5  8 & = 0.4375  1 \\\\0& =0&\qquad & 1.4375 & = 1.4375 \\\\\end{array}[/tex]
The diagram below shows that the graph of g(x) intersects that of the parabola ƒ(x) at x = 1.7 and x = 4.