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Interpreting Quadratic Functions in Standard Form

Interpreting Quadratic Functions in Standard Form 1.13 - Solution

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Quadratic functions can be written in standard form. We know that determines the width and if the graph is upward or downward, and gives the -intercept. Let's begin with the graphs of and , which have a positive value for the coefficient .


The functions and have positive coefficients in front of . We see directly that we can discard since the two graphs have vertical intercepts for and not for . Further, is somewhat wider than , which in this case means that the value of is smaller. Since is less than , we can determine how the expressions fits the graphs.


The functions and has negative coefficients in front of . We are to pair and with two of these: We can discard since the -intercept is clearly below Another thing, observe that is much wider than , which means that it should have a less negative -value than . Then you can see that must be associated with and with .


Thus, we have paired the graphs and functions in the following manner.