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What is the the vertex of #y = (x -3)^2+4x-5 #?

Answer 1

The solution set(or vertex set) is: #S = {-5,-21}.#

The standard formula of the quadratic function is: #y = Ax^2 + Bx +C#

#(x-3)^2# is a notable product, so do this: Square the first number -(signal inside the parenthesis) 2 * first number * second number + second number squared #x^2 - 6x + 9#

Now, substitute it the main equation: #y = x^2 - 6x + 9 +4x - 5 = x^2 +10x +4#, so #y = x^2 +10x +4# #to# Now, it agrees with the standard formula.

To find the point of the vertex in #x# axis, we apply this formula: #x_(vertex) = -b/(2a) = -10/2 = -5#

To find the point of the vertex in #y# axis, we apply this formula: #y_(vertex) = - triangle/(4a) = - (b^2 - 4ac)/(4a) = -(100 -4 * 1 * 4)/4 = -21#

Then, the solution set(or vertex set) is: #S = {-5,-21}.#

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Answer 2

Kennedy Adams

To find the vertex of (y = (x - 3)^2 + 4x - 5), we first rewrite the equation in the standard form (y = a(x - h)^2 + k). This involves expanding the squared term and then regrouping the terms to isolate the squared term. Once in standard form, the vertex of the parabola is at the point ((h, k)).

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Answer from HIX Tutor

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.