1. The first problem asks to sketch the function $f(x) = (x - 5)^2$. 2. This is a parabola that opens upwards with its vertex at the point $(5, 0)$. 3. The general form of a parabola is $f(x) = (x - h)^2$ where $(h, 0)$ is the vertex. 4. Here, $h = 5$, so the vertex is at $(5, 0)$. 5. To sketch, plot the vertex and a few points around it, for example: - At $x=4$, $f(4) = (4-5)^2 = 1$ - At $x=6$, $f(6) = (6-5)^2 = 1$ - At $x=3$, $f(3) = (3-5)^2 = 4$ - At $x=7$, $f(7) = (7-5)^2 = 4$ 6. Connect these points with a smooth curve opening upwards. 7. The second problem asks to graph and label $y = |x|$ and $y = |2x|$. 8. The function $y = |x|$ is a V-shaped graph with vertex at $(0,0)$. 9. The function $y = |2x|$ is similar but steeper because of the factor 2. 10. For $y = |x|$, points include: - $(0,0)$, $(1,1)$, $(-1,1)$ 11. For $y = |2x|$, points include: - $(0,0)$, $(1,2)$, $(-1,2)$ 12. Plot these points and connect with straight lines forming V shapes. Final answers: - $f(x) = (x-5)^2$ is a parabola with vertex at $(5,0)$. - $y = |x|$ and $y = |2x|$ are V-shaped graphs with vertices at $(0,0)$, the latter steeper.