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A day full of math games & activities. Find one near you.
Which zero pair could be added to the function f(x) = x2 + 12x + 6 so that the function can be written in vertex form?
3, -3; 6, -6; 9, -9; 36, -36
Solution:
f(x) = x2 + 12x + 6
It can be written as
y = x2 + 12x + 6
Now convert the standard form to vertex form. The vertex form of a parabola is y = a ( x − h ) 2 + k
First complete the squares and separate x2 and x terms.
y - 6 = x2 + 12x
y - 6 + (-12/2)2= x2 + 12x+(-12/2)2
Add 36 on both sides of the equation
y - 6 + 36 = x2 + 12x + 36
By further calculation
y + 30 = (x + 6)2
So we get the vertex form as
y = (x + 6)2 - 30
Therefore, the zero pairs 36, -36 can be added to the function.
Which zero pair could be added to the function f(x) = x2 + 12x + 6 so that the function can be written in vertex form?
3, -3; 6, -6; 9, -9; 36, -36
Summary:
The zero pair that could be added to the function f(x) = x2 + 12x + 6 so that the function can be written in vertex form is 36, -36
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