document.write( "Question 554523: Hello, I'm having problem graphing g(x)=-7(x+3)^(2)-3 on a number line. Can you help me? Thank you. \n" ); document.write( "

Algebra.Com's Answer #361374 by KMST(5328) $\"\"$ $\"About$

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You cannot graph an function on a number line. You need an x-axis and a y-axis.
\n" ); document.write( "Each x value is associated with a y=f(x) value to determine a point (x, y).
\n" ); document.write( "You can pick a few values for x, make the corresponding (x,y pairs), and plot them.
\n" ); document.write( "If you do not know what the graph will look like, picking random points may not give you a good graph. A graphing calculator or some graphing software program could do it for you.
\n" ); document.write( "The function you have is a quadratic function (meaning a polynomial with degree 2). The graph is a parabola.
\n" ); document.write( "In your case, the graph will look like an arch (like the one in St. Louis or half of the McDonald's logo).
\n" ); document.write( "For x=-3, $\"g%28-3%29=-7%28-3%2B3%29%5E2-3=-3\"$ That is a maximum of the function.
\n" ); document.write( "For any other value of x, $\"%28x%2B3%29%5E2%3E0\"$ ,
\n" ); document.write( " $\"-7%28x%2B3%29%5E2%3C0\"$ and $\"g%28x%29=-7%28x%2B3%29%5E%282%29-3%3C-3\"$ .
\n" ); document.write( "The function is symmetrical to both sides of x=-3. The values of $\"%28x%2B3%29%5E2\"$ and the values of g(x) are the same for -4 as for -2. They are the same for -5 as for -1. They are the same for -6 and for 0. They are the same for pairs of values of x that are the same distance to either side of x=-3.
\n" ); document.write( "The graph looks like this: $\"graph%28300%2C300%2C-7%2C1%2C-45%2C5%2C-7%28x%2B3%29%5E2-3%29\"$
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