Question

Question #e5f61

Answer 1

Plot the solutions at `x=1,3`; plot the vertex at `(2,1)`; plot the y-intercept at `y=-3`, and you've got the graph!
graph{-x^2+4x-3 [-10, 10, -5, 5]}

Explanation:

You can find the solutions with the quadratic formula: `(-4+-sqrt(4^2-4(-1*-3)))/(2*-1)=2+--1=1,3`
The `y`-intercept is easy to find by putting `0` in for `x`, so the `y`-intercept is at `(0,-3)`.

Finally, plot the vertex by solving for the `x`-coordinate with `x=-b/(2a)=(-4)/(2*-1)=2`. Substitute `2` for `x` in the original equation to get the `y`-coordinate of the vertex: `-2^2+4(2)-3=1` So the vertex is at `(2,1)`.

If you need more points, make a table of values using numbers near the x-coordinate of the vertex.
Hope that helps!