f(x)= -X^2-2x+1 find the roots using the quadratic formula label the axis of symmetry and vertex

Question

also give the X and Y intercetps and be able to graph, thanks.

Answer 1

Given f (x ) = - x ^2 - 2x + 1

y  = - x ^2 - 2x + 1

Compare it to parabola equation y  = ax ^2 + bx + c.

a = -1, b  = -2, c  = 1

Axis of symmetry x  = -b /2a  = -(-2)/2(-1) = -1

Axis of symmetry x = -1.

To find vertex substitute the x  value in y  = -x ^2 - 2x + 1.

y  = -(-1)^2 - 2(-1) + 1

y  = -1 + 2 + 1

y = 2

Vertex of parabola = (x  , y  ) = (-1,2).

y = - x ^2 - 2x + 1

To find roots compare it to quadratic equation ax ^2 + bx + c = 0.

a = -1, b = -2, c = 1.

Roots are x  = -2.41 and x  = 0.41.

x intercepts (-2.41,0) and (0.41,0)

To find y  intercept substitute x = 0 in y = -x^2 - 2x + 1.

y = -(0)^2 - 2(0) + 1

y - intercept is (0,1).

Graph

Draw the coordinate plane.

Plot the vetex, x  - intercepts and y  - intercepts.

Connect the plotted points neatly like curve.

Then formed parabola is indicating f (x ) = -x ^2 - 2x + 1.