Consider the graphs of y=x^2 and y=0.6x^2.
Which graph would be narrower? Why?
The graph of y=x^2 would be narrower than the graph of y=0.6x^2.
This is because the coefficient in front of the x^2 term determines the width of the graph. For y=x^2, the coefficient is 1, which means the graph will be wider compared to the graph of y=0.6x^2 where the coefficient is 0.6.
When the coefficient is less than 1, as in the case of y=0.6x^2, it compresses the graph horizontally, making it narrower.
The graph of y=0.6x^2 would be narrower compared to the graph of y=x^2.
When we compare the two functions, we can see that the coefficient in front of the x^2 term is smaller in the equation y=0.6x^2 compared to the equation y=x^2.
Since the coefficient affects the shape of the parabola, a smaller coefficient (0.6 in this case) means that the y-values increase at a slower rate as x increases. This results in a narrower parabola as compared to the parabola with a larger coefficient (1 in this case) where the y-values increase at a faster rate.
To determine which graph is narrower between y = x^2 and y = 0.6x^2, we need to compare their coefficients.
The general form of a quadratic equation is y = ax^2 + bx + c, where "a" represents the coefficient of the squared term.
In this case, y = x^2 has a coefficient "a" of 1, while y = 0.6x^2 has a coefficient "a" of 0.6.
Since the coefficient determines the shape of the parabola, we can conclude that y = 0.6x^2 would be narrower compared to y = x^2.
The reason is that a larger coefficient "a" makes the parabola steeper and narrower, while a smaller coefficient "a" makes the parabola wider. Having a coefficient of 0.6 in y = 0.6x^2 means that the parabola will be narrower compared to y = x^2.
In summary, the graph of y = 0.6x^2 would be narrower than the graph of y = x^2 because it has a smaller coefficient for the squared term.