sophadof
  • sophadof
Quadratic Functions. Solve each by graphing. A) y=x^2+2x-3 B) y=-2x^2-8x+10
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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welshfella
  • welshfella
You can use the Desmos Graphing online feature to draw these graphs. The solutions are the values of x where the graphs cut the x-axis.
sophadof
  • sophadof
I have to show how i got it though.....How i got which points were on the graph @welshfella
Michele_Laino
  • Michele_Laino
question A) hint: I rewrite the quadratic function as follows: \[\begin{gathered} y = {x^2} + 2x - 3 \hfill \\ y = {x^2} + 2x + 4 - 4 - 3 \hfill \\ y = {\left( {x + 2} \right)^2} - 7 \hfill \\ y + 7 = {\left( {x + 2} \right)^2} \hfill \\ \end{gathered} \]

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Michele_Laino
  • Michele_Laino
Now, if I make this traslation: \(Y=y+7\), \(X=x+2\), where \(X,Y\) are the new coordinates, then I get: \(Y=X^2\)
sophadof
  • sophadof
oh ok!!
Michele_Laino
  • Michele_Laino
The graph of the function of \(Y=X^2\), is: |dw:1447100905704:dw| Now, we have to understand where is located the origin of the coordinate system \(X,Y\)
Michele_Laino
  • Michele_Laino
In order to do that, we set \(X=0,Y=0\) into my traslation above: \[\left\{ \begin{gathered} Y = y + 7 \hfill \\ X = x + 2 \hfill \\ \end{gathered} \right.\] So I get: \[\left\{ \begin{gathered} 0 = y + 7 \hfill \\ 0 = x + 2 \hfill \\ \end{gathered} \right.\] please solve for \(x,y\)
Michele_Laino
  • Michele_Laino
oops.. sorry I have made a typo, here are the right formulas: \[\begin{gathered} y = {x^2} + 2x - 3 \hfill \\ y = {x^2} + 2x + 1 - 1 - 3 \hfill \\ y = {\left( {x + 2} \right)^2} - 4 \hfill \\ y + 4 = {\left( {x + 1} \right)^2} \hfill \\ \left\{ \begin{gathered} Y = y + 4 \hfill \\ X = x + 1 \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} \] so please solve this system with respect to \(x,y\): \[\left\{ \begin{gathered} 0 = y + 4 \hfill \\ 0 = x + 1 \hfill \\ \end{gathered} \right.\]
Michele_Laino
  • Michele_Laino
please read the third step as follows: \[y = {\left( {x + 1} \right)^2} - 4\]
sophadof
  • sophadof
ok

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