Question

How do you write `y=-x^2-2x+3` in vertex form and identify the vertex, y intercept and x intercept?

Answer 1

y = -x^2 - 2x + 3

x of vertex: x = (-b/2a) = 2/-2 = -1

y of vertex: f(-1) = -1 + 2 + 3 = 4

Vertex form: `f(x) = -(x + 1)^2 + 4.`

Check by developing: f(x) = -(x^2 + 2x + 1) + 4 = -x^2 - 2x + 3. OK

x-intercepts: y = 0.
Since a + b + c = 0, one real root is `x = 1` and the other is
`x = c/a = -3`