How do you find the axis of symmetry, and the maximum or minimum value of the function #y=x^2+3x-5#?
The axis of symmetry is
The vertex is
Given:
where:
The formula to find the axis of symmetry:
Plug in the known values.
Simplify.
graph{y=x^2+3x-5 [-16.02, 16.01, -8.01, 8.01]}
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The axis of symmetry of the function ( y = x^2 + 3x - 5 ) is given by the formula ( x = -\frac{b}{2a} ), where ( a ) is the coefficient of the quadratic term and ( b ) is the coefficient of the linear term. In this case, ( a = 1 ) and ( b = 3 ), so the axis of symmetry is ( x = -\frac{3}{2} ).
To find the maximum or minimum value of the function, we can evaluate the function at the axis of symmetry. Substitute ( x = -\frac{3}{2} ) into the function to get ( y = (-\frac{3}{2})^2 + 3(-\frac{3}{2}) - 5 = -\frac{17}{4} ).
Therefore, the axis of symmetry is ( x = -\frac{3}{2} ), and the function has a maximum value of ( y = -\frac{17}{4} ) at that point.
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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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