How do you use the important points to sketch the graph of # f(x)= -x^2-3x-6#?
Delta=b^2-4ac# "Check the discriminant"
Blue "maximum / minimum" #color
"If "a<0," then the maximum amount "nnn#
a=-1<0rArrnnn#"here"
"coordinates of vertex" #color(blue)
(color(red)"vertex")=(-3/2)^2-3(-3/2)-6=-15/4#
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To sketch the graph of ( f(x) = -x^2 - 3x - 6 ), follow these steps:
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Identify the vertex: The vertex of the parabola is given by ( (\frac{-b}{2a}, f(\frac{-b}{2a})) ). In this case, ( a = -1 ) and ( b = -3 ). So, ( x = \frac{-(-3)}{2(-1)} = \frac{3}{-2} = -\frac{3}{2} ). Plug this value of ( x ) into the function to find the corresponding ( y )-coordinate.
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Find the ( y )-intercept: Set ( x = 0 ) and solve for ( y ).
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Find the ( x )-intercepts: Set ( f(x) = 0 ) and solve for ( x ).
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Plot the vertex, ( y )-intercept, and ( x )-intercepts on the coordinate plane.
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Determine the direction of the parabola: Since the coefficient of ( x^2 ) is negative, the parabola opens downwards.
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Sketch the graph using the important points and the direction of the parabola.
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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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