Answer:
[tex]y=(x-5)^2+3[/tex]
Step-by-step explanation:
equation has a graph that is a parabola with a vertex at (5, 3)
Given the vertex is (5,3) that is (h,k)
Vertex form of equation is
[tex]y=a(x-h)^2+k[/tex] where (h,k) is the vertex
Given the vertex is (5,3), h=5 and k=3
Plug in the values in the vertex form of the equation
[tex]y=a(x-h)^2+k[/tex]
[tex]y=(x-5)^2+3[/tex]
The equation of graph that has parabola with vertex at (5,3) is y = (x - 5)² + 3
To answer the question, we ned to know what the equation of a parabola is
The equation of a parabola with vertex (h,k) is given by
y = a(x - h)² + k
Since we want to find the equation of parabola that has a vertex at (5, 3).
Since (h, k) is the vertex, (h, k) = (5, 3).
So,
Substituting the values of the variables into the equation, we have
y = a(x - h)² + k
y = a(x - 5)² + 3
Comparing this to the options, a = 1.
So, the required equation of parabola is y = (x - 5)² + 3
Learn more about equation of parabola in vertex form here:
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