Answer:
Step-by-step explanation:
The shape of this graph is that of a parabola. In this case the parabola opens down. The general form of the equation of such a parabola is
y = a(x - h)^2 + k, where (h, k) is the vertex and a is a coefficient to be determined.
In this particular case we can obtain the coordinates of the vertex (h, k) from the graph. They are (3, 4). Thus, h = 3 and k = 4. The graph goes through (1.5, 0). Use this information to determine the value of the coefficient a:
Then the equation of this parabola must be y = a(x - 3)^2 + 4.
0 = a(1.5 - 3)^2 + 4
Then:
0 = a(-1.5)^2 + 4, or
0 = 2.25a + 4, or
2.25a = -4, or
a = 16/9
Thus, the final result: The equation of this parabola is
y = (16/9)(x - 3)^2 + 4
whose graph is a parabola that opens down and has vertex (3, 4).
