help? For y = x2 − 4x + 3, Determine if the parabola opens up or down. State if the vertex will be a maximum or minimum. Find the vertex. Find the x-intercepts. Describe the graph of the equation. Show all work and use complete sentences
the leading coefficient is positive (it is one) so it opens up
that means the second coordinate of the vertex will be a minimum
first coordinate of the vertex of \(ax^2+bx+c\) is \(-\frac{b}{2a}\) which in your case is \[-\frac{-4}{2\times 1}=2\] second coordinate is what you get for y when you replace \(x\) by \(2\)
x intercepts solve \[ x^2 − 4x + 3=0\] which is easy in this case because it factors
i will leave the complete sentence nonsense up to you i barely speak inglish but here is a nice picture http://www.wolframalpha.com/input/?i=x^2-4x%2B3
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