If $y = f (x)$ is quadratic polynomial having vertex at $(6, 8),$ as shown in the figure below, then $f (x)$ is

x^{2} + 8 x - 76

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x^{2} - 10 x + 32

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x^{2} - 4 x - 4

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x^{2} - 12 x + 44

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Solution

The correct option is D $x^{2} - 12 x + 44$
Graph of $y = x^{2}$ is

Now shifting the graph by $6$ units right side, we get
$\Rightarrow y = {(x - 6)}^{2}$

Now, shifting this curve upwards by $8$ units, we get
$\Rightarrow y = {(x - 6)}^{2} + 8$

Hence, the required equation of the curve is
$y = (x - 6)^{2} + 8 \Rightarrow y = x^{2} - 12 x + 36 + 8 ∴ y = x^{2} - 12 x + 44$

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If y=f(x) is quadratic polynomial having vertex at (6,8), as shown in the figure below, then f(x) is

The correct option is D x2−12x+44Graph of y=x2 is Now shifting the graph by 6 units right side, we get ⇒y=(x−6)2 Now, shifting this curve upwards by 8 units, we get ⇒y=(x−6)2+8 Hence, the required equation of the curve is y=(x−6)2+8⇒y=x2−12x+36+8∴y=x2−12x+44

If $y = f (x)$ is quadratic polynomial having vertex at $(6, 8),$ as shown in the figure below, then $f (x)$ is