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Without graphing how can you tell which slope is steeper?
For a positive number, as the slope(y=mx+b where m is the slope) gets greater in value, the line gets steeper when plotted on a graph. For a negative number, as the slope(y=mx+b where m is the slope) gets greater in value, the line gets less steep when plotted on a graph.
What happens to a line when the slope gets bigger and bigger?
As m, in the equation y=mx+b, gets bigger the line begins to get steeper.
Why is it okay for a graph to cross one of its's horizontal asymptotes?
There is nothing in the definition of "asymptote" that forbids a graph to cross its asymptote. The only requirement for a line to be an asymptote is that if one of the coordinates gets larger and larger, the graph gets closer and closer to the asymptote. The "closer and closer" part is defined via limits.
How does changing the sign of the leading coefficient in an equation of the form y equals ax2 affect its graph?
It gets reflected in the x-axis.
What does changing the a variable do to the graph of a quadratic?
I assume this question refers to the coefficient of the squared term in a quadratic and not a variable (as stated in the question). That is, it refers to the a in ax2 + bx + c where x is the variable.When a is a very large positive number, the graph is a very narrow or steep-sided cup shape. As a become smaller, the graph gets wider until, when a equals zero (and the equation is no longer a quadratic) the graph is a horizontal line. Then as a becomes negative, the graph becomes cap shaped. As the magnitude of a increases, the sides of the graph become steeper.
