Respuesta :
Answer:
U=1-5(x-2)^2
Step-by-step explanation:
The equation of the parabola with vertex (h,k) is y=a(−h+x)2+k
Thus, the equation of the parabola is y=a(x−2)2+1
To find a, use the fact that the parabola passes through the point (3,−4): −4=a+1
Solving this equation, we get that a=−5
Thus, the equation of the parabola is y=1−5(x−2)^2
The equation of the parabola is:
[tex]y = -5(x - 2)^2 + 1[/tex]
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The vertex-form equation of a parabola of vertex (h,k) is given by:
[tex]y = a(x - h)^2 + k^2[/tex]
In this problem:
- Vertex (2,1), thus [tex]h = 2, k = 1[/tex].
[tex]y = a(x - 2)^2 + 1[/tex]
Point (3,-4) means that when [tex]x = 3, y = -4[/tex], and this is used to find a.
[tex]y = a(x - 2)^2 + 1[/tex]
[tex]-4 = a(3 - 2)^2 + 1[/tex]
[tex]a + 1 = -4[/tex]
[tex]a = -5[/tex]
Thus, the equation is:
[tex]y = -5(x - 2)^2 + 1[/tex]
A similar problem is given at https://brainly.com/question/17987697
