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Write an equation of a parabola with a vertex at (4, -1) in vertex form. ​

Sagot :

semsee45

Answer:

[tex]y=2(x-4)^2-1[/tex]

Step-by-step explanation:

The vertex form of a parabola is:

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

To write an equation of a parabola with a vertex at (4, -1) in vertex form, substitute h = 4 and k = -1 into the formula:

[tex]y=a(x-4)^2-1[/tex]

We can choose any value of a. Let's use a = 2:

[tex]y=2(x-4)^2-1[/tex]

Therefore, an equation of a parabola with a vertex at (4, -1) in vertex form is:

[tex]\Large\boxed{\boxed{y=2(x-4)^2-1}}[/tex]

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