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Suppose a parabola has vertex (6,5) and also passes through the point (7,7). Write the equation of the parabola in vertex form.

A. y=(x-6)^2+5
B. y=2(x-6)^2+5
C. y=2(x+6)^2+5
D. y=2(x-6)^2-5

Sagot :

Jacob193idn

Answer:

Choice B: [tex]y = 2\, (x - 6)^{2} + 5[/tex].

Step-by-step explanation:

For a parabola with vertex [tex](h,\, k)[/tex], the vertex form equation of that parabola in would be:

[tex]\text{$y = a\, (x - h)^{2} + k$ for some constant $a$}[/tex].

In this question, the vertex is [tex](6,\, 5)[/tex], such that [tex]h = 6[/tex] and [tex]k = 5[/tex]. There would exist a constant [tex]a[/tex] such that the equation of this parabola would be:

[tex]y = a\, (x - 6)^{2} + 5[/tex].

The next step is to find the value of the constant [tex]a[/tex].

Given that this parabola includes the point [tex](7,\, 7)[/tex], [tex]x = 7[/tex] and [tex]y = 7[/tex] would need to satisfy the equation of this parabola, [tex]y = a\, (x - 6)^{2} + 5[/tex].

Substitute these two values into the equation for this parabola:

[tex]7 = (7 - 6)^{2}\, a + 5[/tex].

Solve this equation for [tex]a[/tex]:

[tex]7 = a + 5[/tex].

[tex]a = 2[/tex].

Hence, the equation of this parabola would be:

[tex]y = 2\, (x - 6)^{2} + 5[/tex].

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