# How do you find the zeros, if any, of #y= -x^2 -3x +17 #using the quadratic formula?

Let's apply the quadratic formula:

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To find the zeros of the quadratic function ( y = -x^2 - 3x + 17 ) using the quadratic formula:

- Identify the coefficients ( a = -1 ), ( b = -3 ), and ( c = 17 ).
- Substitute these values into the quadratic formula: ( x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} ).
- Calculate the discriminant, ( b^2 - 4ac ).
- If the discriminant is positive, there are two real roots. If it's zero, there's one real root (a repeated root). If it's negative, there are no real roots (two complex roots).
- Substitute the values of ( a ), ( b ), and ( c ) into the quadratic formula and solve for ( x ).

The quadratic formula is:

[ x = \frac{{-(-3) \pm \sqrt{{(-3)^2 - 4(-1)(17)}}}}{{2(-1)}} ]

[ x = \frac{{3 \pm \sqrt{{9 + 68}}}}{{-2}} ]

[ x = \frac{{3 \pm \sqrt{{77}}}}{{-2}} ]

Therefore, the zeros of the function are:

[ x = \frac{{3 + \sqrt{{77}}}}{{-2}} ] and [ x = \frac{{3 - \sqrt{{77}}}}{{-2}} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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