Problem

$x^{2}+14 x-16 y+17=0$ write in standard form

Answer

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Answer

The standard form of the given equation is \(\boxed{y = \frac{x^{2}}{16} + \frac{7x}{8} + \frac{17}{16}}\).

Steps

Step 1 :Given the equation \(x^{2}+14 x-16 y+17=0\).

Step 2 :We need to write this equation in standard form. The standard form of a quadratic equation is \(ax^2 + bx + c = 0\).

Step 3 :To do this, we rearrange the given equation by moving the term involving \(y\) to the other side of the equation.

Step 4 :This gives us the equation \(x^{2} + 14x + 17 = 16y\).

Step 5 :Finally, we simplify the equation to get the standard form.

Step 6 :The standard form of the given equation is \(\boxed{y = \frac{x^{2}}{16} + \frac{7x}{8} + \frac{17}{16}}\).

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