graph the equation $y=-x^{2}+4x - 3$ on the accompanying set of axes. you must plot 5 points including the…

Explanation:

Step1: Find the roots

Set (y = 0), so (-x^{2}+4x - 3=0). Multiply through by (- 1) to get (x^{2}-4x + 3=0). Factor: ((x - 1)(x - 3)=0). So (x=1) or (x = 3). The root points are ((1,0)) and ((3,0)).

Step2: Find the vertex

For a quadratic (y=ax^{2}+bx + c), the (x) - coordinate of the vertex is (x=-\frac{b}{2a}). Here (a=-1), (b = 4), so (x=-\frac{4}{2\times(-1)} = 2). Substitute (x = 2) into (y=-x^{2}+4x - 3): (y=-(2)^{2}+4\times2-3=-4 + 8-3=1). The vertex is ((2,1)).

Step3: Find two more points

Let (x=0), then (y=-0^{2}+4\times0-3=-3), so the point is ((0,-3)). Let (x = 4), then (y=-(4)^{2}+4\times4-3=-16 + 16-3=-3), so the point is ((4,-3)).

Answer:

The five points to plot are ((0,-3)), ((1,0)), ((2,1)), ((3,0)), ((4,-3)).