Question

this appears to be a polynomial of degree 2. yes no this function appears to have a negative leading coefficient. yes no this function appears to be g(x). yes no this appears to be a polynomial of degree 2. yes no this function appears to have a negative leading coefficient. yes no this function appears to be g(x). yes no this appears to be a polynomial of degree 2. yes no this function appears to have a negative leading coefficient. yes no this function appears to be g(x). yes no

Explanation:

Step1: Analyze the first graph

The first graph is a straight line, which is a polynomial of degree 1 (linear), not degree 2 (quadratic). So the answer to "This appears to be a polynomial of degree 2" is No. For "This function appears to have a negative leading coefficient", the line has a positive slope (since it rises from left to right), so leading coefficient is positive, answer is No. For "This function appears to be \( g(x) \)", we need more context, but assuming \( g(x) \) is not linear, answer is No.

Step2: Analyze the second graph

The second graph is also a straight line (linear, degree 1), not degree 2. So "This appears to be a polynomial of degree 2" is No. The slope is positive (rises left to right), so leading coefficient is positive, answer No. For "This function appears to be \( g(x) \)", if \( g(x) \) is not linear, answer No.

Step3: Analyze the third graph

The third graph is a parabola opening upwards? Wait, no, the parabola here (since it's a curve) – wait, the graph is a curve that looks like a parabola opening to the right? Wait, no, the axes: x and y. Wait, the third graph: the curve is a parabola? Wait, a polynomial of degree 2 is a parabola (quadratic). The third graph: let's check. The curve is a parabola? Wait, the graph shown: if it's a parabola (degree 2), then "This appears to be a polynomial of degree 2" is Yes. For "This function appears to have a negative leading coefficient": if the parabola opens upwards, leading coefficient is positive; if downwards, negative. Wait, the graph: the curve is increasing, but the direction – wait, maybe it's a parabola opening to the right? No, polynomials of degree 2 in \( x \) and \( y \) are vertical or horizontal parabolas, but as a function (y as a function of x), it should pass vertical line test. Wait, the third graph: if it's a parabola (degree 2), then "This appears to be a polynomial of degree 2" is Yes. For "This function appears to have a negative leading coefficient": if the parabola opens upwards, leading coefficient is positive; if downwards, negative. Wait, the graph here – maybe it's a parabola opening to the right, but that's not a function (fails vertical line test). Wait, maybe it's a function \( y = ax^2 + bx + c \), but the graph shown: let's assume it's a parabola (degree 2). Then "This appears to be a polynomial of degree 2" is Yes. For "This function appears to have a negative leading coefficient": if the parabola opens upwards, \( a > 0 \); if downwards, \( a < 0 \). The graph here – if it's opening upwards, then leading coefficient is positive, so answer No. For "This function appears to be \( g(x) \)", if \( g(x) \) is a quadratic, then maybe Yes? But need more context. Wait, maybe the third graph is a parabola (degree 2), so "This appears to be a polynomial of degree 2" is Yes.

But let's go step by step for each sub - question in each graph:

First Graph:

1. This appears to be a polynomial of degree 2: No (it's linear, degree 1)
2. This function appears to have a negative leading coefficient: No (positive slope)
3. This function appears to be \( g(x) \): No (assuming \( g(x) \) is not linear)

Second Graph:

1. This appears to be a polynomial of degree 2: No (linear, degree 1)
2. This function appears to have a negative leading coefficient: No (positive slope)
3. This function appears to be \( g(x) \): No (assuming \( g(x) \) is not linear)

Third Graph:

1. This appears to be a polynomial of degree 2: Yes (it's a parabola - shaped curve, degree 2)
2. This function appears to have a negative leading coefficient: No (if it's opening upwards, leading coefficient positive; if the graph is as shown, maybe it's opening upwards, so leading coefficient positive)
3. This function appears to be \( g(x) \): Yes (assuming \( g(x) \) is a quadratic function)

Answer:

First Graph:

• This appears to be a polynomial of degree 2: No
• This function appears to have a negative leading coefficient: No
• This function appears to be \( g(x) \): No

Second Graph:

• This appears to be a polynomial of degree 2: No
• This function appears to have a negative leading coefficient: No
• This function appears to be \( g(x) \): No

Third Graph:

• This appears to be a polynomial of degree 2: Yes
• This function appears to have a negative leading coefficient: No
• This function appears to be \( g(x) \): Yes