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Alebra, pick all the equations that represent the graph below, there is 3 answers

Alebra, pick all the equations that represent the graph below, there is 3 answers-example-1

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There are a few ways to work this one.

The first thing to know is that if (1,0) is an x-intercept, then (x-1) will be a factor in the factored version. So this makes the first answer correct and the second one not:

Yes: y = 3(x-1)(x-3)

No: y = 3(x+1)(x+3)

The second thing to know is that if (h,k) is the vertex, then equation in vertex form will be y = a (x-h)^2 + k.

Since (2,-3) is the vertex, then the equation would be y = a (x-2)^2 -3.

This makes the third answer correct and the fourth not:

Yes: y = 3(x-2)^2 - 3

No: y = 3(x+2)^2 + 3

By default, this means that the last answer must work, since you said there are 3 answers.

We can confirm it is correct (and not a trick question) by factoring the last answer:

y = 3x^2 - 12x +9

= 3 (x^2 -4x +3)

= 3 (x-3)(x-1)

And this matches our first answer.

User Rowan San
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