Question

question 9 of 16 (1 point) | question attempt: 2 of unlimit
your answer is incorrect.

• (b): your answer is incorrect.
• (c): your answer is incorrect.
• (d) x - intercept(s): your answer is incorrect.
• (d) y - intercept(s): your answer is incorrect.

use the graph of the parabola to fill in the table.
(a) does the parabola open upward or downward?
upward downward
(b) find the equation of the axis of symmetry.
equation of axis of symmetry: ( x = - 3 )
(c) find the coordinates of the vertex.
vertex: ( (-3,-1) )
(d) find the intercept(s).
for both the x - and y - intercept(s), make sure to do the following.

• if there is more than one, separate them with commas.
• if there are none, select

one\.
x - intercept(s): - 4, - 2
y - intercept(s): 2

Explanation:

Step1: Determine the axis of symmetry

The axis of symmetry of a parabola passes through its vertex. From the graph, the vertex is at \(x = - 2\) (since the vertex is the lowest point of the upward - opening parabola and its \(x\) - coordinate is \(x=-2\)). So the equation of the axis of symmetry is \(x=-2\).

Step2: Determine the vertex coordinates

The vertex of the parabola is the lowest point. From the graph, the vertex has coordinates \((-2,-1)\) (the \(x\) - coordinate is from the axis of symmetry and the \(y\) - coordinate is the \(y\) - value of the lowest point).

Step3: Determine the \(x\) - intercepts

The \(x\) - intercepts are the points where the parabola crosses the \(x\) - axis (\(y = 0\)). From the graph, the parabola crosses the \(x\) - axis at \(x=-3\) and \(x=-1\) (the points \((-3,0)\) and \((-1,0)\)).

Step4: Determine the \(y\) - intercept

The \(y\) - intercept is the point where the parabola crosses the \(y\) - axis (\(x = 0\)). From the graph, when \(x = 0\), \(y=3\) (the point \((0,3)\)).

Answer:

(b) equation of axis of symmetry: \(x=-2\)
(c) vertex: \((-2,-1)\)
(d) \(x\) - intercept(s): \(-3,-1\); \(y\) - intercept(s): \(3\)