Question

1. for the provided graph of a parabola, determine key features and record them in the table.

direction of opening
number of zeroes
location of zeroes
y - intercept
axis of symmetry
max/min value
vertex

1. for the provided graph of a parabola, determine key features and record them in the table.

direction of opening
number of zeroes
location of zeroes
y - intercept
axis of symmetry
max/min value
vertex

1. for the provided graph of a parabola, determine key features and record them in the table.

direction of opening
number of zeroes
location of zeroes
y - intercept
axis of symmetry
max/min value
vertex

Explanation:

Step1: Analyze problem 5

For the parabola opening downwards:

• The number of zero - es is 2 as it crosses the x - axis at two points.
• To find the location of zeroes, identify x - values where the graph intersects the x - axis. From the graph, they seem to be around $x=- 8$ and $x = 0$.
• The y - intercept is the value of y when $x = 0$. From the graph, $y=-2$.
• The axis of symmetry for a parabola $y = ax^{2}+bx + c$ is $x=-\frac{b}{2a}$, and for a graph, it is the vertical line passing through the vertex. By visual inspection, the axis of symmetry is $x=-4$.
• Since it opens downwards, it has a maximum value. The maximum value is the y - coordinate of the vertex, which is $y = 2$.
• The vertex is the point where the parabola reaches its maximum value, which is $(-4,2)$.

Step2: Analyze problem 6

For the parabola opening upwards:

• The number of zero - es is 2 as it crosses the x - axis at two points.
• The location of zeroes: By observing the graph, they are around $x=-9$ and $x = 3$.
• The y - intercept is the value of y when $x = 0$. From the graph, $y=-3$.
• The axis of symmetry is the vertical line passing through the vertex. By visual inspection, it is $x=-3$.
• Since it opens upwards, it has a minimum value. The minimum value is the y - coordinate of the vertex, which is $y=-4$.
• The vertex is the point where the parabola reaches its minimum value, which is $(-3,-4)$.

Answer:

Problem 5

Feature	Value
Number of Zeroes	2
Location of Zeroes	$x=-8,x = 0$
y - intercept	$y=-2$
Axis of Symmetry	$x=-4$
Max/Min Value	$y = 2$ (Max)
Vertex	$(-4,2)$

Problem 6

Feature	Value
Number of Zeroes	2
Location of Zeroes	$x=-9,x = 3$
y - intercept	$y=-3$
Axis of Symmetry	$x=-3$
Max/Min Value	$y=-4$ (Min)
Vertex	$(-3,-4)$