Question

use the graph of the parabola to fill in the table.
(a) does the parabola open upward or downward?
upward downward
(b) 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):
y-intercept(s):
(c) find the coordinates of the vertex.
vertex: ( , )
(d) find the equation of the axis of symmetry.
equation of axis of symmetry:

Explanation:

Step1: Determine parabola direction

A parabola opens downward if its vertex is the maximum point (the graph curves downward). From the graph, the parabola has a peak (vertex) and opens downward. So the answer for (a) is downward.

Step2: Find x - intercepts

x - intercepts are where the graph crosses the x - axis. Looking at the graph, it seems to cross the x - axis at \(x=-1\) and \(x = 3\) (assuming the grid lines are at integer values). So x - intercepts are \(-1,3\).

Step3: Find y - intercept

y - intercept is where the graph crosses the y - axis. The graph crosses the y - axis at \(y=-6\) (since when \(x = 0\), \(y=-6\)). So y - intercept is \(-6\).

Step4: Find vertex coordinates

The vertex is the highest point of the downward - opening parabola. The x - coordinate of the vertex is the mid - point of the x - intercepts. Mid - point of \(-1\) and \(3\) is \(\frac{-1 + 3}{2}=\frac{2}{2}=1\). The y - coordinate can be found from the graph (the peak). Let's assume from the graph that at \(x = 1\), \(y=-4\). So vertex is \((1,-4)\).

Step5: Find axis of symmetry

The axis of symmetry of a parabola is a vertical line passing through the vertex. The equation of a vertical line is \(x = h\), where \(h\) is the x - coordinate of the vertex. Since the vertex has \(x = 1\), the axis of symmetry is \(x = 1\).

Answer:

(a) downward
(b) x - intercept(s): \(-1,3\); y - intercept(s): \(-6\)
(c) vertex: \((1,-4)\)
(d) equation of axis of symmetry: \(x = 1\)