Answered

Find solutions to your problems with the help of IDNLearn.com's expert community. Discover in-depth answers from knowledgeable professionals, providing you with the information you need.

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].

Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.