Questions: Find the x-intercepts and y-intercepts for f(x). f(x) = x^2 - 4x + 1 Find the x-intercepts for f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The x-intercept(s) is(are) . (Type an ordered pair. Simplify your answer. Type an exact answer, using radicals as needed. Use commas to separate answers as needed.) B. There is no x-intercept. Find the y-intercepts for f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept(s) is(are) . (Type an ordered pair. Type an exact answer in simplified form. Use commas to separate answers as needed.) B. There is no y-intercept.

Find the x-intercepts and y-intercepts for f(x).
f(x) = x^2 - 4x + 1

Find the x-intercepts for f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The x-intercept(s) is(are) .
(Type an ordered pair. Simplify your answer. Type an exact answer, using radicals as needed. Use commas to separate answers as needed.)
B. There is no x-intercept.

Find the y-intercepts for f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The y-intercept(s) is(are) .
(Type an ordered pair. Type an exact answer in simplified form. Use commas to separate answers as needed.)
B. There is no y-intercept.

Transcript text: Find the $x$-intercepts and $y$-intercepts for $f(x)$. \[ f(x)=x^{2}-4 x+1 \] Find the $x$-intercepts for $f(x)$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $x$-intercept(s) is(are) $\square$ . (Type an ordered pair. Simplify your answer. Type an exact answer, using radicals as needed. Use commas to separate answers as needed.) B. There is no $x$-intercept. Find the $y$-intercepts for $f(x)$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $y$-intercept(s) is(are) $\square$ . (Type an ordered pair. Type an exact answer in simplified form. Use commas to separate answers as needed.) B. There is no $y$-intercept.

Solution

Solution Steps

To find the intercepts of the function $ f(x) = x^2 - 4x + 1 $, we need to determine where the graph of the function crosses the x-axis and y-axis.

X-intercepts: Set $ f(x) = 0 $ and solve the quadratic equation $ x^2 - 4x + 1 = 0 $ for $ x $. This will give the x-coordinates where the graph intersects the x-axis.
Y-intercepts: Evaluate $ f(x) $ at $ x = 0 $ to find the y-coordinate where the graph intersects the y-axis.

Step 1: Find the X-Intercepts

To find the x-intercepts of the function $ f(x) = x^2 - 4x + 1 $, we set $ f(x) = 0 $: \[ x^2 - 4x + 1 = 0 \] The solutions to this equation are: \[ x = 2 - \sqrt{3} \quad \text{and} \quad x = 2 + \sqrt{3} \]

Step 2: Find the Y-Intercept

To find the y-intercept, we evaluate the function at $ x = 0 $: \[ f(0) = 0^2 - 4(0) + 1 = 1 \] Thus, the y-intercept is $ 1 $.