Question

How do I find the vertex, axis of symmetry, y-intercept, x-intercept, domain and range of `y=-x^2+2x-5`?

Answer 1

y = -x^2 + 2x - 5

Explanation:

y = -x^2 + 2x - 5
x-coordinate of vertex and axis of symmetry:
x = (-b/2a) = -2/-2 = 1
y-coordinate of vertex:
y(1) = -1 + 2 - 5 = -4
y-intercept. Make x = 0 --> y = -5
x-intercepts. Make y = 0 -->Solve -x^2 + 2x - 5 = 0.
Since D = 4 - 20 < 0, there are no real roots (no x-intercepts)
The graph is a parabola that opens downward (a < 0), and that is completely below the x-axis. It has a minimum. (-4) at vertex (1, -4).
Domain of x (-infinity, infinity)
Range of y (-infinity, -4)and (-4, -infinity)
graph{-x^2 + 2x - 5 [-20, 20, -10, 10]}