Question

exit ticket november 6 vertex for
true or false
the
parabola has
a minimum
vertex
the
parabola is
opening
downwards
the vertex
and y-
intercept are
at the same
point
the axis of
symmetry is
x = 5
the vertex is
the
maximum
the
parabola has
one x-
intercept
true false

Explanation:

Step1: Analyze the parabola's vertex type

For a parabola, if it opens upwards, the vertex is a minimum; if it opens downwards, the vertex is a maximum. From the graph, the parabola opens downwards, so it has a maximum vertex. So, "The parabola has a minimum vertex" is False.

Step2: Determine the direction of the parabola's opening

By observing the graph, the parabola opens downwards. So, "The parabola is opening downwards" is True.

Step3: Check the vertex and y - intercept

The vertex of the parabola is at \((0,5)\) (from the graph). The y - intercept is the value of \(y\) when \(x = 0\). For this parabola, when \(x=0\), \(y = 5\). So the vertex \((0,5)\) and y - intercept (at \(x = 0,y=5\)) are at the same point. So, "The vertex and y - intercept are at the same point" is True.

Step4: Find the axis of symmetry

The axis of symmetry of a parabola \(y=ax^{2}+bx + c\) is given by \(x=-\frac{b}{2a}\). For a parabola symmetric about the y - axis (\(x = 0\)) (since the vertex is at \(x = 0\) and the parabola is symmetric about the vertical line passing through the vertex). So, "The axis of symmetry is \(x = 5\)" is False.

Step5: Analyze the vertex as a maximum

Since the parabola opens downwards, the vertex is the maximum point. So, "The vertex is the maximum" is True.

Step6: Count the x - intercepts

The x - intercepts are the points where \(y = 0\). From the graph, the parabola crosses the x - axis at two points (\(x=-3\) and \(x = 3\)). So, "The parabola has one x - intercept" is False.

Answer:

1. False
2. True
3. True
4. False
5. True
6. False