How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y=-x^2+6x-2#?
Maximum
Axis of symmetry
Given -
#y=-x^2+6x-2#
Vertex -
#x=(-b)/(2a)=(-6)/(2 xx (-1))=(-6)/(-2)=3#
#y=-(3)^2+6(3)-2=-9+18-2=18-11=7#
#(3, 7)#
Axis of symmetry -
#x=3#
How to graph?
After finding the vertex, take a few points on either side of
Find the corresponding y values.
Graph them
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To find the axis of symmetry of a quadratic function in the form (y = ax^2 + bx + c), use the formula: (x = -\frac{b}{2a}).
For the given function (y = -x^2 + 6x - 2), (a = -1) and (b = 6).
Substitute these values into the formula: (x = -\frac{6}{2(-1)} = -\frac{6}{-2} = 3).
So, the axis of symmetry is (x = 3).
To find the vertex, substitute (x = 3) into the function: (y = -(3)^2 + 6(3) - 2 = -9 + 18 - 2 = 7).
Thus, the vertex is ( (3, 7)).
Since the coefficient of (x^2) is negative, the parabola opens downwards, and the vertex represents the maximum value of the function.
So, the maximum value of the function is (y = 7), which occurs at (x = 3).
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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.
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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