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denis23 [38]
3 years ago
13

Write the quadratic function in standard form. f(x) = 6x^2 − x + 1

Mathematics
1 answer:
AlexFokin [52]3 years ago
4 0

Answer:

The equation in standard form is:

f(x)=6(x-\frac{1}{12})^2-\frac{23}{24}

Step-by-step explanation:

Given function:

f(x)=6x^2-x+1

We need to convert this in standard form which is given by:

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

where a represent co-efficient of leading term which is x^2

and (h,k) is the vertex (minimum and maximum point) of the curve.

h can be found out using formula h=\frac{-b}{2a}

a=6\ and\  b=-1

h=\frac{-(-1)}{2(6)}=\frac{1}{12}

We can find k by finding f(h) as k=f(h).

k=f(\frac{1}{12})=6(\frac{1}{12})^2-\frac{1}{12}+1

k=(6\times \frac{1}{144})-\frac{1}{12}+1

k=\frac{1}{24}-\frac{1}{12}+1

k=\frac{1-2+24}{24}=\frac{23}{24}

Thus the equation in standard form is:

f(x)=6(x-\frac{1}{12})^2-\frac{23}{24}

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