Answer:
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
