Question

(a) classify the shape of the curve. oval parabola line circle (b) state the location of the vertex. (x, y) = ( ) (c) find the equation for the axis of symmetry. (d) state the location of the y - intercept. (x, y) = ( ) (e) state the locations of the x - intercepts. (x, y) = ( ) (smaller x - value) (x, y) = ( ) (larger x - value)

Explanation:

Step1: Identify vertex

By observing the graph of the parabola, the vertex is the lowest - point. Visually, it is at $(-1,-2)$. So $(x,y)=(-1,-2)$.

Step2: Find axis of symmetry

The axis of symmetry of a parabola passes through the vertex. For a parabola opening vertically, the equation of the axis of symmetry is $x =$ the $x$-coordinate of the vertex. So the equation is $x=-1$.

Step3: Determine y - intercept

The $y$-intercept is the point where the graph crosses the $y$-axis (i.e., when $x = 0$). By looking at the graph, when $x = 0$, $y=-1$. So $(x,y)=(0,-1)$.

Step4: Find x - intercepts

The $x$-intercepts are the points where the graph crosses the $x$-axis (i.e., when $y = 0$). By observing the graph, the smaller $x$-value for the $x$-intercept is $x=-3$ and the larger $x$-value is $x = 1$. So $(x,y)=(-3,0)$ (smaller $x$-value) and $(x,y)=(1,0)$ (larger $x$-value).

Answer:

(b) $(-1,-2)$
(c) $x=-1$
(d) $(0,-1)$
(e) $(-3,0)$
$(1,0)$