How do you write #y = 4x^2 8x +9# in vertex form?
See below.
Vertex forms is:
We want to make the equation like this.
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To write the quadratic function ( y = 4x^2  8x + 9 ) in vertex form, complete the square:

Factor out the coefficient of ( x^2 ) from the first two terms: [ y = 4(x^2  2x) + 9 ]

Complete the square inside the parentheses by adding and subtracting ((\frac{2}{2})^2 = 1): [ y = 4(x^2  2x + 1  1) + 9 ]

Group the terms and simplify: [ y = 4((x  1)^2  1) + 9 ]

Expand and combine like terms: [ y = 4(x  1)^2  4 + 9 ]

Simplify the constant terms: [ y = 4(x  1)^2 + 5 ]
Therefore, the vertex form of the quadratic function is ( y = 4(x  1)^2 + 5 ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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