Answer:
a. opens: downward
b. vertex: (4, 2)
c. x-intercepts: (2, 0), (6, 0); y-intercept: (0, -6)
d. a.o.s.: x = 4
Step-by-step explanation:
A:
Based on the picture the parabola opens downwards. Right away you know that the "a" value in the parabola's equation will be negative.
B:
To find the coordinates of the vertex, you'll need to look at the picture. Remember: look on the x-axis first and then the y-axis next.
The very top of the parabola (maximum point = vertex) is at the x-value of 4 and the y-value of 2. This means the coordinates of the vertex of this parabola is (4, 2).
C:
To find the x-intercepts, look at the x-axis and see where the parabola crosses it. The parabola goes through the x-axis at the x-values of 2 and 6, so the x-intercepts of this parabola are (2, 0) and (6, 0).
To find the y-intercept, look at the y-axis and see where the parabola crosses it. The parabola intersects the y-axis at the y-value of -6, so (0, -6) would be the y-intercept.
D:
The equation for the axis of symmetry of a graph is always x = h, where h is the x-value of the coordinate of the vertex.
Since the vertex is (4, 2), where 4 = h, the equation of the axis of symmetry would be x = 4.
