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Start by identifying a, b, and c. The maximum value of the given quadratic function is f ( - b2a ).
Maximum Value: 1
Domain: All real numbers
Range: y ≤ 1
Increasing Interval: To the left of x=1
Decreasing Interval: To the right of x=1
For the quadratic function f(x)=ax^2+bx+c, the y-coordinate of the vertex is the maximum value of the function when a<0.
We can see above that a= - 2, b= 4, and c= - 1. We will now use these values to find the desired information.
a= - 2, b= 4
a(- b)=- a * b
- a/- b= a/b
Calculate quotient
x= 1
Calculate power
Multiply
Add and subtract terms
Unless there are any specified restrictions on the x-values, the domain of a quadratic function is all real numbers. Therefore, the domain of this function is all real numbers. Furthermore, since a= - 2 is less than 0, the range is all values less than or equal to the maximum value, 1. Domain:& All real numbers Range:& y ≤ 1
Since a= - 2 is less than 0, the function increases to the left of the maximum value and decreases to the right of the maximum value, which we know occurs at 1. Increasing Interval:& To the left of 1 Decreasing Interval:& To the right of 1