Respuesta :
[tex]\bf y=\pm(x-{{ h}})^2+{{ k}}\qquad\qquad vertex\ ({{ h}},{{ k}})\\\\
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f(x)=x^2\iff y=(x-0)^2+0\\\\\\ f(x)=-x^2\iff y=-(x-0)^2+0[/tex]
if the maximum, or minimum is at 5, that simply means y = 5 and x =-2 for the vertex of that parabola
so just set h= -2 and k = 5 there, that's the parabola's equation
if the maximum, or minimum is at 5, that simply means y = 5 and x =-2 for the vertex of that parabola
so just set h= -2 and k = 5 there, that's the parabola's equation
The equation in a standard form of the parabola that has a maximum at y = 5 is y = (x + 2)² + 5.
What is the parabola?
It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
Write an equation in a standard form of the parabola that has the same shape as the graph of f(x)=4x² or g(x)=−4x², but with the given maximum or minimum.
y (Maximum) = 5 at x = −2
Then the equation of the parabola is given as
y = (x - h)² + k
Then we have
h = -2 and k = 5, then the equation will be
y = (x + 2)² + 5
More about the parabola link is given below.
https://brainly.com/question/8495504
