The graph of the quadratic function y=-x^2-2x+3 is shown below

The axis of symmetry is at

The graph has an x-intercept at

The graph has a vertex at

Step-by-step explanation:

we have

Statements

case 1) The graph has root at and

The statement is False

Because, the roots of the quadratic equation are the values of x when the value of y is equal to zero (x-intercepts)

Observing the graph, the roots are at and

case 2) The axis of symmetry is at

The statement is True

Observing the graph, the vertex is the point

The axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex

so

the equation of the axis of symmetry is

case 3) The graph has an x-intercept at

The statement is True

see procedure case 1)

case 4)  The graph has an y-intercept at

The statement is False

Because, the y-intercept is the value of y when the value of x is equal to zero

Observing the graph, the y-intercept is the point

case 5) The graph has a relative minimum at

The statement is False

Because, is a vertical parabola open downward, therefore the vertex is a maximum

The point represent the vertex of the parabola, so is a maximum

case 6) The graph has a vertex at

The statement is True

see the procedure case 5)

see the attached figure to better understand the problem

i suppose it should be (y=2x-5)

step-by-step explanation: