Question

Help please!!!!!!!!!!!!!!!!!!!!!!!!!

Given ​ f(x)=x2−12x+46​.




Enter the quadratic function in vertex form











What is the axis of symmetry for f(x)=3^2 + 9x + 15?


x = −3/2


x = -2


x = −2/3

Answer 1

`\large\boxed{1.\ f(x)=(x-6)^2+10}\\\\\boxed{2.\ x=-(3)/(2)}`

Explanation:

The quadratic function:

`f(x)=ax^2+bx+c`

1.

The vertex form of a quadratic function:

`f(x)=a(x-h)^2+k`

`h=(-b)/(2a)\\\\k=f(h)`

We have

`f(x)=x^2-12x+46\\\\a=1,\ b=-12,\ c=46`

Substitute:

`h=(-(-12))/(2(1))=(12)/(2)=6\\\\k=f(6)=6^2-12(6)+46=36-72+46=10\\\\f(x)=1(x-6)^2+10`

2.

The equation of an axis of symmetry:

`x=(-b)/(2a)`

We have:

`f(x)=3x^2+9x+15\\\\a=3,\ b=9,\ c=15`

Substitute:

`x=(-9)/(2(3))=-(3)/(2)`