can some one help me with this i've been studying for hours this is my last question and im tired
Create your own quadratic equation that has an axis of symmetry of x = 1 and whose graph opens down. Then find the vertex, domain, range, and x-intercepts. Show all work to receive full credit.
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Start with a standard quadratic equation: \[
y = x^2
\]It has an axis of symmetry at 0, so we'll fix that by shifting it over \(1\) horizontally.
This is done by replacing \(x\) with \(x-1\). \[
y = (x-1)^2
\]Now the problem is that it opens up. We can reflect it vertically by multiplying it by -1. \[
y = -(x-1)^2
And we're done. We can expand it using foil if we want. \[
y = -x^2+2x-1