Which of the following has a graph that is wider than the graph of y=3x^2+2?
A) y=3x^2+3
B) y=0.5x^2+1
C) y=-4x^2-1
D) y=4x^2+1
If anyone could help that would be amazing. Thank you so much!
probably, but I'm not sure what you mean by "wider." All the graphs stretch out both directions infinitely far.
However, (B) does so more slowly, so I guess you could say it's wider. See
http://www.wolframalpha.com/input/?i=plot+y%3D3x^2%2B2%2C+y%3D3x^2%2B3%2C+y%3D0.5x^2%2B1%2C+y%3D-4x^2-1%2C+y%3D4x^2%2B1+
Is the answer B?
To determine which equation has a graph wider than the graph of y=3x^2+2, we need to compare the coefficients of x^2 in each equation.
The equation y=3x^2+2 has a coefficient of 3 for x^2.
Let's compare the coefficients of x^2 for each equation:
A) y=3x^2+3 --> The coefficient of x^2 is 3, which is the same as in the original equation y=3x^2+2.
B) y=0.5x^2+1 --> The coefficient of x^2 is 0.5 which is less than 3, so the graph is narrower.
C) y=-4x^2-1 --> The coefficient of x^2 is -4 which is less than 3, so the graph is narrower.
D) y=4x^2+1 --> The coefficient of x^2 is 4 which is greater than 3, so the graph is wider than y=3x^2+2.
Therefore, the equation y=4x^2+1 has a graph that is wider than the graph of y=3x^2+2. The answer is D) y=4x^2+1.
To determine which of the given equations has a graph wider than y=3x^2+2, we need to compare the coefficients of x^2 in each equation.
The graph of y=3x^2+2 represents a parabola with the coefficient of x^2 equal to 3.
Let's analyze each equation:
A) y=3x^2+3 - The coefficient of x^2 is 3, same as the original equation. Therefore, the graph will have the same width.
B) y=0.5x^2+1 - The coefficient of x^2 is 0.5, which is smaller than 3. Therefore, the graph will be narrower.
C) y=-4x^2-1 - The coefficient of x^2 is -4, which is larger than 3. This means the graph will be wider.
D) y=4x^2+1 - The coefficient of x^2 is 4, which is larger than 3. So, the graph will be wider.
From the analysis above, options C) and D) have graphs wider than y=3x^2+2. Thus, the correct answer is either option C) or D).