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Which values of a, b, and c make f(x) = 5(x +4)2 - 2 equivalent to a function in the form f(x) = ax? +bx+c?
A a =5, b = 40, C = 78
(B) a = 5, b = 0, C = 78
Ca = 5, b = 40, C = 80
Da = 5, b = 0, C = 80



Answer :

ozieltijerina
Here you go!! Hope this helps
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By simplifying quadratic function  [tex]f(x)= 5(x+4)^2-2[/tex]  and comparing coefficient with standard form of quadratic function [tex]f(x) = ax^2 +bx+c[/tex] we got   a = 5,b=40 and c=78

What is quadratic function ?

A function of the form  [tex]f(x) = ax^2 + bx + c,[/tex]  where a, b, and c are real numbers and a not equal to zero is known as quadratic function.

Given function is

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

We can covert it into standard form of quadratic function as

[tex]f(x)= 5( x^2+2\times x\times 4+4^2)-2\\\\\\\Rightarrow f(x)= 5( x^2+8x+16)-2\\\\\Rightarrow f(x)= 5 x^2+40x+80-2\\\\\\\\\Rightarrow f(x)= 5 x^2+40x+78\\\\\\[/tex]

Now we can get value of a ,b and c by comparing coefficient

[tex]f(x) = ax^2 +bx+c[/tex]  with   [tex]f(x)= 5 x^2+40x+78[/tex]

So a = 5,b=40 and c=78

By simplifying quadratic function  [tex]f(x)= 5(x+4)^2-2[/tex]  and comparing coefficient with standard form of quadratic function [tex]f(x) = ax^2 +bx+c[/tex] we got   a = 5,b=40 and c=78

To learn more about  quadratic function visit :https://brainly.com/question/4119784