Given:
The graph of a quadratic function
.
To find:
(a) The coordinates of the turning point.
(b) The roots of the equation
Solution:
(a)
From the given graph it is clear that first the graph is decreasing after that it is increasing. So, the minimum point is the turning point.
The turning is at (2,-1) because the distance between the turning point from the y-axis is 2 and from the x-axis is 1 in the downward direction.
Therefore, the coordinates of the turning point are (2,-1).
(b)
The x-intercepts are the roots of an equation because roots are the x-coordinates of the points where the graph intersect the x-axis.
From the given graph it is clear the graph intersect the x-axis at x=1 and x=3.
Therefore, the roots of the given equation are 1 and 3.