How do you find the maximum value of #y = −2x^2 − 3x + 2#?
The maximum value of the function is
We can tell two things about this function before we begin approaching the problem:
 The polynomial is of degree two, meaning it changes direction only once. Thus, the only point at which is changes direction must also be our maximum. In a higher degree polynomial, it might be necessary to compute multiple local maxima and determine which is the largest.
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To find the maximum value of ( y = 2x^2  3x + 2 ), you can use the vertex formula for a quadratic function. The vertex of a parabola in the form ( y = ax^2 + bx + c ) is given by:
[ x = \frac{b}{2a} ]
Substitute the values of ( a ) and ( b ) from the equation ( y = 2x^2  3x + 2 ) into the vertex formula to find the xcoordinate of the vertex. Then, substitute this xcoordinate into the original equation to find the corresponding ycoordinate.

Determine the values of ( a ) and ( b ): ( a = 2 ) and ( b = 3 )

Apply the vertex formula to find the xcoordinate of the vertex: ( x = \frac{b}{2a} = \frac{3}{2(2)} = \frac{3}{4} )

Substitute ( x = \frac{3}{4} ) into the original equation to find the corresponding ycoordinate: ( y = 2\left(\frac{3}{4}\right)^2  3\left(\frac{3}{4}\right) + 2 )

Calculate ( y ): ( y = 2\left(\frac{9}{16}\right)  3\left(\frac{3}{4}\right) + 2 = \frac{9}{8}  \frac{9}{4} + 2 = \frac{9}{8}  \frac{18}{8} + \frac{16}{8} = \frac{11}{8} )
So, the maximum value of the function ( y = 2x^2  3x + 2 ) occurs when ( x = \frac{3}{4} ) and ( y = \frac{11}{8} ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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