Question

1. y=(x - 3)^2+2

vertex:
axis of symmetry:
opens: up down
maximum minimum
max/min value:
y - intercept:

Explanation:

Step1: Identify vertex form of parabola

The equation $y=(x - 3)^2+2$ is in vertex - form $y=a(x - h)^2+k$, where $(h,k)$ is the vertex. Here $h = 3$ and $k = 2$, so the vertex is $(3,2)$.

Step2: Find axis of symmetry

For a parabola in the form $y=a(x - h)^2+k$, the axis of symmetry is the vertical line $x = h$. So the axis of symmetry is $x = 3$.

Step3: Determine max/min

Since $a = 1>0$, the parabola opens up, and it has a minimum value. The minimum value is the $y$ - coordinate of the vertex, which is $y = 2$.

Step4: Find y - intercept

To find the y - intercept, set $x = 0$. Then $y=(0 - 3)^2+2=9 + 2=11$.

Answer:

Vertex: $(3,2)$
Axis of symmetry: $x = 3$
Opens: up
Maximum/Minimum: Minimum
Max/Min Value: $2$
y - intercept: $11$