The graph of equation 1/2(x+1)=[tex](y-5)^{2}[/tex] looks like graph of a horizontal parabola.
What is equation?
Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.
How to graph equation?
one-half(x + 1) = (y – 5)^2, written symbolically, is (1/2)(x - [-1]) = [tex](y-5)^{2}[/tex]
or x + 1 = 2[tex](y-5)^{2}[/tex]. Because the y term is squared, we know immediately that the graph is a horizontal (not vertical) parabola.
This equation can be written as
x = 2[tex](y-5)^{2}[/tex] - 1
The standard equation of a horizontal parabola with vertex (h, k) is
x = c[tex](c-k)^{2}[/tex] + h. Comparing this to the given quadratic:
we see that k = 5 and h = -1. This tells us that the vertex of this graph is (-1, 5), and that the graph is stretched horizontally because c = 2 is greater than 1.
To graph this, it's best to make a short table of points, as follows, remembering that y is the independent value and x depends on y through the equation given above.
y x = 2[tex](y-5)^{2}[/tex] - 1 (x, y)
0 x = 49 (49, 0)
2 x = 2(-3)^2 - 1 (17, 2)
1 x = 2(-4)^2 - 1 (31, 1)
vertex (already found) (-1, 5)
Learn more about equation at https://brainly.com/question/2972832
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