How do you find the important points to graph $y = f (x) = x^{2} + 1$ $y=f(x)=x^2+1$ ?

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How do you find the important points to graph $y = f (x) = x^{2} + 1$ $y=f(x)=x^2+1$ ?

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Answer 1 · 2017-03-28T18:41:58

$x^{2} + 1$ $x^2+1$ tells us something important. On the parent graph of $x^{2}$ $x^2$ , the important points are $x = 0$ $x=0$ , $y = 0$ $y=0$ . The $+ 1$ $+1$ in this equation tells us that it's the same graph, except it has been shifted up one unit. So instead of $(0, 0)$ $(0,0)$ , now the x-intercept is $(0, 1)$ $(0, 1)$ . All the normal points in $x^{2}$ $x^2$ have kept their $x$ $x$ values, but the $y$ $y$ values have increased by $1$ $1$ .

We can check that in this graph.

graph{y=x^2}
graph{y=x^2+1}

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How do you find the important points to graph $y = f (x) = x^{2} + 1$ $y=f(x)=x^2+1$ ?

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How do you find the important points to graph $y = f (x) = x^{2} + 1$ $y=f(x)=x^2+1$ ?