Question

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

Answer 1

B, C, F

The axis of symmetry is x= -1

The graph has an x-intercept at (1,0)

The graph has a vertex at (-1,4)

Explanation:

just did that quiz and those were the correct ones :)

Answer 2

The axis of symmetry is at
`x=-1`

The graph has an x-intercept at
`(1,0)`

The graph has a vertex at
`(-1,4)`

Explanation:

we have

`y=-x^(2)-2x+3`

Statements

case 1) The graph has root at
`3` and
`1`

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
`-3` and
`1`

case 2) The axis of symmetry is at
`x=-1`

The statement is True

Observing the graph, the vertex is the point
`(-1,4)`

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
`x=-1`

case 3) The graph has an x-intercept at
`(1,0)`

The statement is True

see procedure case 1)

case 4) The graph has an y-intercept at
`(-3,0)`

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
`(0,3)`

case 5) The graph has a relative minimum at
`(-1,4)`

The statement is False

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

The point
`(-1,4)` represent the vertex of the parabola, so is a maximum

case 6) The graph has a vertex at
`(-1,4)`

The statement is True

see the procedure case 5)

see the attached figure to better understand the problem