Question

answer the questions about the quadratic function above.
the function opens up.
the vertex of the function is (-1, 8).
the quadratic function has a minimum.
the y - intercept of the quadratic function is (-1, 8).

Explanation:

To solve the questions about the quadratic function, we analyze the graph:

1. Direction of Opening

A parabola opens down if it has a maximum point (the vertex is the highest point) and opens up if it has a minimum point (the vertex is the lowest point). From the graph, the parabola opens downward (the arrows point down, and the vertex is the peak). So the correct option is "down" (not "up").

2. Vertex of the Function

The vertex is the highest (or lowest) point of the parabola. From the graph, the vertex appears to be at \((-1, 8)\) (this part was correct in the original, as the peak is at \(x = -1\), \(y = 8\)).

3. Maximum or Minimum

Since the parabola opens downward, it has a maximum (the vertex is the highest point, so the function reaches a maximum value there). The original "minimum" is incorrect; it should be "maximum".

4. \(y\)-intercept

The \(y\)-intercept is the point where the graph crosses the \(y\)-axis (where \(x = 0\)). From the graph, when \(x = 0\), the \(y\)-value is \(7\) (or visually, the graph crosses the \(y\)-axis at \((0, 7)\), not \((-1, 8)\)). The original \((-1, 8)\) is incorrect (that is the vertex, not the \(y\)-intercept).

Corrected Answers:

• The function opens: \(\boldsymbol{\text{down}}\)
• The Vertex of the function is: \(\boldsymbol{(-1, 8)}\) (correct)
• The quadratic function has a: \(\boldsymbol{\text{maximum}}\)
• The \(y\)-intercept of the quadratic function is: \(\boldsymbol{(0, 7)}\) (or the \(y\)-value when \(x = 0\), visible on the graph)

If we focus on correcting the errors:

• Opening direction: down (not up)
• Maximum/minimum: maximum (not minimum)
• \(y\)-intercept: \((0, 7)\) (not \((-1, 8)\))

The vertex \((-1, 8)\) was correct.

Answer:

To solve the questions about the quadratic function, we analyze the graph:

1. Direction of Opening

A parabola opens down if it has a maximum point (the vertex is the highest point) and opens up if it has a minimum point (the vertex is the lowest point). From the graph, the parabola opens downward (the arrows point down, and the vertex is the peak). So the correct option is "down" (not "up").

2. Vertex of the Function

The vertex is the highest (or lowest) point of the parabola. From the graph, the vertex appears to be at \((-1, 8)\) (this part was correct in the original, as the peak is at \(x = -1\), \(y = 8\)).

3. Maximum or Minimum

Since the parabola opens downward, it has a maximum (the vertex is the highest point, so the function reaches a maximum value there). The original "minimum" is incorrect; it should be "maximum".

4. \(y\)-intercept

The \(y\)-intercept is the point where the graph crosses the \(y\)-axis (where \(x = 0\)). From the graph, when \(x = 0\), the \(y\)-value is \(7\) (or visually, the graph crosses the \(y\)-axis at \((0, 7)\), not \((-1, 8)\)). The original \((-1, 8)\) is incorrect (that is the vertex, not the \(y\)-intercept).

Corrected Answers:

• The function opens: \(\boldsymbol{\text{down}}\)
• The Vertex of the function is: \(\boldsymbol{(-1, 8)}\) (correct)
• The quadratic function has a: \(\boldsymbol{\text{maximum}}\)
• The \(y\)-intercept of the quadratic function is: \(\boldsymbol{(0, 7)}\) (or the \(y\)-value when \(x = 0\), visible on the graph)

If we focus on correcting the errors:

• Opening direction: down (not up)
• Maximum/minimum: maximum (not minimum)
• \(y\)-intercept: \((0, 7)\) (not \((-1, 8)\))

The vertex \((-1, 8)\) was correct.