Question

a table of values for $y=(x-1)^2$ is shown. what features can be found using the table of values?$square$ $x$-intercepts$square$ $y$-intercepts$square$ vertex$square$ axis of symmetry$square$ increasing/decreasing$square$ positive/negative| $x$ | $-1$ | $0$ | $1$ | $2$ | $3$ || --- | --- | --- | --- | --- | --- || $y$ | $4$ | $1$ | $0$ | $1$ | $4$ |

Explanation:

Step1: Identify x-intercepts

Look for $y=0$: When $x=1$, $y=0$.

Step2: Identify y-intercepts

Look for $x=0$: When $x=0$, $y=1$.

Step3: Locate the vertex

Find the minimum $y$-value: $y=0$ at $x=1$.

Step4: Find axis of symmetry

Axis is $x$-coordinate of vertex: $x=1$.

Step5: Determine increasing/decreasing

For $x<1$, $y$ decreases as $x$ increases; for $x>1$, $y$ increases as $x$ increases.

Step6: Check positive/negative

All $y$-values are non-negative, positive except at $x=1$.

Answer:

• x-intercepts: $(1, 0)$
• y-intercepts: $(0, 1)$
• vertex: $(1, 0)$
• axis of symmetry: $x=1$
• increasing/decreasing: Decreasing for $x<1$, increasing for $x>1$
• positive/negative: Positive for all $x

eq1$, zero at $x=1$