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Write an equation in vertex form of a parabola with a vertex at (-2, 6)

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Semsee45idn

Answer:

y = (x + 2)² + 6

Step-by-step explanation:

To write an equation in vertex form of a parabola with a vertex at (-2, 6), we can use the following formula:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Vertex form of a quadratic equation}}\\\\y=a(x-h)^2+k\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$(h,k)$ is the vertex.}\\\phantom{ww}\bullet\;\textsf{$a$ is the leading coefficient.}\end{array}}[/tex]

In this case:

  • h = -2
  • k = 6

Substitute the values of h and k into the formula, and use any value for a. Let's use a = 1:

[tex]y=1(x-(-2))^2+6\\\\y=(x+2)^2+6[/tex]

So, an equation in vertex form of a parabola with a vertex at (-2, 6) is:

[tex]\Large\boxed{\boxed{y=(x+2)^2+6}}[/tex]

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