Questions: Without graphing, find the x - and y-intercepts for f(x). f(x)=x^2-8x+2 Select the correct choice below and fill in any answer boxes in your choice. A. There is no x-intercept. B. The x-intercept(s) are (Type an integer or decimal rounded to the nearest tenth as needed. Use a comma to separate answers as needed.) A. The y-intercept(s) are . (Type an integer or decimal rounded to the nearest tenth as needed. Use a comma to separate answers as needed.) B. There is no y-intercept.

Without graphing, find the x - and y-intercepts for f(x).
f(x)=x^2-8x+2

Select the correct choice below and fill in any answer boxes in your choice.
A. There is no x-intercept.
B. The x-intercept(s) are
(Type an integer or decimal rounded to the nearest tenth as needed. Use a comma to separate answers as needed.)
A. The y-intercept(s) are .
(Type an integer or decimal rounded to the nearest tenth as needed. Use a comma to separate answers as needed.)
B. There is no y-intercept.

Transcript text: Without graphing, find the $x$ - and $y$-intercepts for $f(x)$. \[ f(x)=x^{2}-8 x+2 \] Select the correct choice below and fill in any answer boxes in your choice. A. There is no x-intercept. B. The $x$-intercept(s) are $\square$ (Type an integer or decimal rounded to the nearest tenth as needed. Use a comma to separate answers as needed.) A. The y-intercept(s) are $\square$ . (Type an integer or decimal rounded to the nearest tenth as needed. Use a comma to separate answers as needed.) B. There is no y-intercept.

Solution

Solution Steps

Step 1: Finding $x$-intercepts

To find the $x$-intercepts of the function $f(x) = x^2 - 8x + 2$, we set $f(x) = 0$ and solve the quadratic equation. The discriminant, $\Delta = b^2 - 4ac = -8^2 - 4\cdot1\cdot2 = 56$, determines the nature of the roots. Since $\Delta > 0$, there are two distinct real x-intercepts at x = 7.7 and x = 0.3.

Step 2: Finding $y$-intercept

To find the $y$-intercept, we set $x = 0$ in the function, which gives $f(0) = 2$. Therefore, the $y$-intercept is always at the point $(0, 2)$.