How do you find the vertex and the intercepts for #y= (x-4) (x+2)#?
See below
The y-coordinate is found by plugging our answer back into the equation:
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To find the vertex and intercepts for ( y = (x - 4)(x + 2) ):
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Vertex: The vertex of a quadratic function in the form ( y = ax^2 + bx + c ) is at ( x = -\frac{b}{2a} ). In this case, ( a = 1 ) and ( b = -2 ), so the x-coordinate of the vertex is ( x = -\frac{-2}{2(1)} = 1 ). Substitute ( x = 1 ) into the equation to find the y-coordinate of the vertex: ( y = (1 - 4)(1 + 2) = (-3)(3) = -9 ). Therefore, the vertex is at (1, -9).
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x-intercepts (or roots): Set ( y = 0 ) and solve for ( x ): ( (x - 4)(x + 2) = 0 ). This equation is satisfied when either ( x - 4 = 0 ) or ( x + 2 = 0 ). Solving these gives ( x = 4 ) and ( x = -2 ). So, the x-intercepts are at ( x = 4 ) and ( x = -2 ).
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y-intercept: Substitute ( x = 0 ) into the equation: ( y = (0 - 4)(0 + 2) = (-4)(2) = -8 ). Therefore, the y-intercept is at (0, -8).
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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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