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The function below is written in vertex form or intercept form. Rewrite them in standard form and show your work.

y = 5(x+3)^2-4

Respuesta :

Answer:

The standard form as [tex]y=5x^2+30x+41[/tex]

Step-by-step explanation:

Given: A function which is written in vertex form or intercept form.

We have to re-write it  in standard form that in terms of

Given [tex]y = 5(x+3)^2-4[/tex]

Squaring  using [tex](a+b)^2=a^2+b^2+2ab[/tex] , we get,  

[tex]y=5(x^2+9+6x)-4[/tex]

Multiply 5 inside , we get,

[tex]y=5x^2+45+30x-4[/tex]

Solving further , we get,

[tex]y=5x^2+30x+41[/tex]

Thus , we have obtained the standard form as [tex]y=5x^2+30x+41[/tex]







Answer: The standard form of equation will be

[tex]f(x)=5x^2+30x+41[/tex]

Step-by-step explanation:

Since we have given that

The vertex form of equation is given by

[tex]y=5(x+3)^2-4[/tex]

We need to find the standard form :

Standard form is written as :

[tex]f(x)=ax^2+bx+c[/tex]

So, our equation becomes,

[tex]y =5(x+3)^2-4\\\\y=5(x^2+9+6x)-4\\\\y=5x^2+45+30x-4\\\\y=5x^2+30x+41[/tex]

Hence, the standard form of equation will be

[tex]f(x)=5x^2+30x+41[/tex]