First, you have to have a clear idea what y = 2x^2+4x-5 means. This is an equation that tells you that, for any value of x, you can find y by dividing by multiplying x by x, and then multiplying that by two, adding 4 times x and finally subtracting 5. Does that sound familiar?  

Now, what is the table you have to make? You will list several values of x (which you will be using as x-coordinates in your graph), and for

each one use the equation to find what y is. We'll show the work:

    For x = 1,    y = 2*1*1    +    4*1   -   5    =    1

    For x = 2,    y = 2*2*2    +    4*2   -   5    =  11

    For x = 3,    y = 2*3*3    +    4*3   -   5    =  25

    For x = 4,    y = 2*4*4    +    4*4   -   5    =  43

    For x = 5,    y = 2*5*5    +    4*5   -   5    =  65

Do you see what we did there? We just replaced x in the equation by each value of x, and did the multiplication and addition.

Now your table will look like this:

    x |  y

    --+-----

    1 | 1

    2 | 11

    3 | 25

    4 | 43

    5 | 65

We’ve only shown the x,y values for 1 through 5, but there are an infinite number of x values that you could plug in, including negative numbers and fractions. You can use the resulting T chart to help you create a graph, which will look like this: