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The family of this graph?

The family of this graph?-example-1
User Alashow
by
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1 Answer

15 votes
15 votes

Answer:

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).

User PlacateTheCattin
by
3.0k points
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