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

##### 1 Answer

Oct 17, 2015

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]}