Problem

Find the maximum value of the quadratic function f(x)=−2x2+4x+3.

Answer

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Answer

f(0.5)=−2(0.5)2+4∗0.5+3=3.5

Steps

Step 1 ：The quadratic function f(x)=ax2+bx+c reaches its maximum or minimum value at x=−b2a. So, let's calculate x=−b2a for f(x)=−2x2+4x+3.

Step 2 ：−b2a=−42∗(−2)=0.5

Step 3 ：Substitute x=0.5 into the function f(x)=−2x2+4x+3 to find the maximum value.

Step 4 ：f(0.5)=−2(0.5)2+4∗0.5+3=3.5

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