can someone explain to me how to write the equation of the quadratic function only using the vertex and roots?

Question

anonymous · Answer

the question on my homework says write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1), please don't give me an answer but help me how to figure it out

ybarrap · Answer

You can start with the equation of a parabola:
$$
y=(x-h)^2+k
$$
Where, <h,k> is the vertex.

anonymous · Answer

y=(x--6)^2+-1?

ybarrap · Answer

That's right, but these produce roots at -5 and -7, not at -3 and -9, so we have to shift our vertex to make these roots. Notice the difference between -5 and -3 and between -7 and -9?

ybarrap · Answer

The difference is -2. So, we need to shift the whole parabola left by 2 units.

anonymous · Answer

so then after shifting the whole parabola what do i do?

ybarrap · Answer

The shifted parabola is our solution. 

Question I have for you is this. We can create two equations. One will have vertex at (-6,-1). We did that. Next, we can create a second equation with root at -3 and -9. Is the question asking you to come up with TWO equations?

anonymous · Answer

only the first one ! thanks :)

ybarrap · Answer

Ok, so you just needed a quadratic with vertex at (-6,-1) then?

goformit100 · Answer

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