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Vikki [24]
3 years ago
9

What is the equation of the graph below? A graph shows a parabola that opens down with a vertex at three comma one. y = − (x − 3

)2 + 1 y = − (x + 1)2 + 4 y = (x + 1)2 − 4 y = (x − 4)2 + 1

Mathematics
1 answer:
vitfil [10]3 years ago
6 0

The option must be:

  • \mathbf{y=-(x-3)^{2}+1}
  • \mathbf{y=-(x+1)^{2}+4}
  • \mathbf{y=(x+1)^{2}-4}
  • \mathbf{y=-(x-4)^{2}+1}

Answer:

\mathbf{y=-(x-3)^{2}+1}

Step-by-step explanation:

There are generally two forms in which quadratic equation is represented:

  1. \mathrm{y=ax^{2}+bx+c}
  2. \mathrm{y=a(x-h)^{2}+k}

The options here are given in the second form, so by interpreting the second form in graphical form will give the the answer.

In second form <em>'</em><em>h' and 'k' are the x-coordinate and y-coordinate respectively of the vertex of parabola</em>.

In the given graph the coordinates of vertex is (3 , 1).

So h = 3 and k = 1.

In the second form <em>'a' decide the direction of opening of parabola</em>, <em>if a is greater than zero than the opening is upward and if a is less than zero than opening of parabola is downwards</em>.

In the given graph the parabola opens downward so the value of a is -1.

a = -1

Therefore the final equation of parabola is as follows:

\mathbf{y=-(x-3)^{2}+1}

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