document.write( "Question 1194535: Mario is going to fly through this scene, following the path of the quadratic function 𝑓(𝑥). Based on the
\n" ); document.write( "table and graph, you will write equations for this quadratic function in each of three forms: standard
\n" ); document.write( "form, vertex form, and factored form. You may start with any form you choose, but you need to write
\n" ); document.write( "equivalent equations in all three forms.
\n" ); document.write( "equivalent equations in all three forms.
\n" ); document.write( "𝑥 𝑓(𝑥)
\n" ); document.write( "0 3
\n" ); document.write( "1 1.25
\n" ); document.write( "2 0
\n" ); document.write( "3 -0.75
\n" ); document.write( "4 -1
\n" ); document.write( "5 -0.75
\n" ); document.write( "6 0
\n" ); document.write( "7 1.25
\n" ); document.write( "8 3
\n" ); document.write( "1. \n" ); document.write( "

Algebra.Com's Answer #826830 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!
Mario is going to fly through this scene, following the path of the quadratic function 𝑓(𝑥). Based on the
\n" ); document.write( "table and graph, you will write equations for this quadratic function in each of three forms: standard
\n" ); document.write( "form, vertex form, and factored form. You may start with any form you choose, but you need to write
\n" ); document.write( "equivalent equations in all three forms.
\n" ); document.write( "equivalent equations in all three forms.
\n" ); document.write( "𝑥 𝑓(𝑥)
\n" ); document.write( "0 3
\n" ); document.write( "1 1.25
\n" ); document.write( "2 0
\n" ); document.write( "3 -0.75
\n" ); document.write( "4 -1
\n" ); document.write( "5 -0.75
\n" ); document.write( "6 0
\n" ); document.write( "7 1.25
\n" ); document.write( "8 3
\n" ); document.write( "1.
\n" ); document.write( "

For this problem, you don't have to go through all that one of the other persons went through to get the VERTEX form of this parabola. It's OVERKILL!\r\n" );
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document.write( "Notice that the y-values on either side of point (4, - 1) repeat (up and down)? This means that (4, - 1) is the VERTEX (h, k) of this parabola. \r\n" );
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document.write( "Vertex form of a PARABOLA: \r\n" );
document.write( "                            ------- Substituting (4, - 1) and (0, 3) for (h, k) and (x, y), respectively\r\n" );
document.write( "                            3 = 16a - 1\r\n" );
document.write( "                        3 + 1 = 16a\r\n" );
document.write( "                            4 = 16a\r\n" );
document.write( "                            \r\n" );
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document.write( "To determine the VERTEX form of this equation, we get:\r\n" );
document.write( "                            ------- Substituting  and (4, - 1) for \"a\", and (h, k), respectively\r\n" );
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document.write( "(2, 0) and (6, 0) are the 2 zeroes, and \"a\" has already been determined. Knowing this, you can now find the other 2 forms!

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