Question

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The table represents a quadratic
X
y
-6 23
-5 8
-4-1
-3-4
-2 -1
-18.
0 23
What is the equation of the function?
Oy=(x+3)²-4
Oy=(x-3)² + 4

Answer 1

`y=ax^(2) +bx+c`

(0, 23) :

`y=ax^(2) +bx+23`

(-1,8) :

`8=a-b+23`

`a-b=-15`

(-2,-1) :

`-1=4a-2b+23`

`4a-2b=-24`

`2a-b=-12`

Elimination

`a-b=-15`

`2a-b=-12`

--------------------- -

`a=3`

`b=18`

Quadratic eq :

`y=3x^(2) +18x+23`

`y=3x^(2) +18x+27-4`

`y=3(x^(2) +6x+9)-4`

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

Explanation: