since all quadratic curves have the same basic shape any quadratic curve can be obtained by performing a series of transformations on the curve y = x 2. Start by writing y = 2 x x – 1 in completed square form: 2 x x – 1 = 2( x x ) – 1 = 2(( x + 1) 2 – 1...
I then ask students if they can find a place in the equation of a quadratic function that reveals each of these graph features. Standard form clearly shows the y-intercept, factored form gives the x-intercepts (if any), and vertex form indicates the high or low point. We use the “trac...
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then common sense says at least one of the two terms has to be zero to start with. So, if you move all the terms over to one side, you can put the quadratics into a form that can be factored, allowing that side of the equation to equal zero. Once you’ve done that, it’s pr...