contestada

The graph of function g is a parabola with the vertex located at (5,9). The parabola also passes through the point (3, 1). Which of the following is an
equation in vertex form for this function?

Respuesta :

I just did this the answer is C. g(x) = –2(x – 5)2 + 9

Ver imagen Camrynmullins527

The required function is [tex]g(x)=-2(x-5)^2+9[/tex].

Important information:

  • Vertex of parabola is at (5,9).
  • Parabola passes through the point (3,1).

We need to find the equation in vertex form for the function g.

Parabola:

The vertex form of a parabola is:

[tex]g(x)=a(x-h)^2+k[/tex]         ...(i)

Where, [tex]a[/tex] is a constant and [tex](h,k)[/tex] is the vertex.

Substitute [tex]h=5,k=9[/tex] in (i).

[tex]g(x)=a(x-5)^2+9[/tex]          ...(ii)

Parabola passes through the point (3,1). So, substitute [tex]x=3,g(x)=1[/tex] in (ii).

[tex]1=a(3-5)^2+9[/tex]

[tex]1-9=a(-2)^2[/tex]

[tex]-8=4a[/tex]

[tex]-2=a[/tex]

Substitute [tex]a=-2[/tex] in (ii).

[tex]g(x)=-2(x-5)^2+9[/tex]

Thus, the required function is [tex]g(x)=-2(x-5)^2+9[/tex].

Find out more about 'parabola' here:

https://brainly.com/question/15165354

Otras preguntas