Think about how the parameters a and c in y=ax^2+c affect the value of the function in comparison to the quadratic function, y=x^2. How do these effects would shown in a graph?
See solution.
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Let's think about how the parameters a and c in y=ax^2+c affect the value of the function in comparison to the quadratic function, y=x^2. Then, we can figure out how these effects would be shown in a graph.
Effect of the Parameter a
Notice that this parameter is multiplying each value of the original function, y=x^2. Therefore, if a<1, the y-values increase faster in comparison to y=x^2. This causes a vertical stretch of the function's graph and gives it a thinner look.
On the other hand, if 0vertically shrunk, getting it a wider look.
Finally, if a=- 1 the y-values become negatives but the points keep the same distance from the x-axis. This produces a reflection across the x-axis.
In general, we can summarize the effects of a.
If |a|>1 the graph is vertically stretched, getting a thinner look.
If 0<|a|<1, the graph is vertically shrunk, getting a wider look.
If a<0, the graph is reflected across the x-axis.
Effects of the Parameter c
Notice that this parameter is adding a constant value to the original function, y=x^2. Therefore, all the y-values increase by the same fixed quantity. This causes the graph of the function to translate vertically — upwards if c>0, and downwards if c<0.
