b) algebraically determine the equation for $f$ in the form $y=\\sqrt{b(x-h)}+k$.\n$4.5 = \\sqrt{b(14-5)} +…
b) algebraically determine the equation for $f$ in the form $y=\\sqrt{b(x-h)}+k$.\n$4.5 = \\sqrt{b(14-5)} + 3$\n$y=\\sqrt{\\frac{1}{4}(x-5)} + 3$
Answer
Explanation:
Step1: Isolate the radical term
Subtract 3 from both sides. $4.5 - 3 = \sqrt{b(14-5)}$ $1.5 = \sqrt{9b}$
Step2: Square both sides
Eliminate the square root. $(1.5)^2 = (\sqrt{9b})^2$ $2.25 = 9b$
Step3: Solve for b
Divide both sides by 9. $b = \frac{2.25}{9} = \frac{1}{4}$
Step4: Substitute b, h, k
Use $h=5$, $k=3$, $b=\frac{1}{4}$ in the given form.
Answer:
$y=\sqrt{\frac{1}{4}(x-5)} + 3$