How do you determine the vertex and direction when given a quadratic function?

Answer 1

There are two forms a quadratic function could be written in: standard or vertex form. Here are the following ways you can determine the vertex and direction dependent on the form:

Standard Form (#f(x)=ax^2 + bx + c#) 1. Direction of the parabola can be determined by the value of a. If a is positive, then the parabola faces up (making a u shaped). If a is negative, then the parabola faces down (upside down u). 2. Vertex can be found by #x= -b/(2a)# and then plugging in that value to find y. Here is an example: #y = -2x^2 + 4x - 3#, Faces downward since a = -2. to find the vertex: #x= (-4)/(2(-2))=(-4)/ (-4) = 1# then plug that value into the equation#y = -2x^2 + 4x - 3# #y = -2(1)^2 + 4(1) - 3 # #y = -2(1) +4(1) - 3 # #y = -2 + 4 -3 # #y = -1 # Vertex is (1,-1)
Vertex Form (#y=a(x-h)^2 +k#) 1. Direction of the parabola can be determined by the value of a. If a is positive, then the parabola faces up (making a u shaped). If a is negative, then the parabola faces down (upside down u). 2. Vertex is (h,k). Here is an example: #y = -3(x-2)+6# Faces down since a = -3 and the vertex is (2, 6).
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Answer 2

To determine the vertex and direction of a quadratic function, you can use the vertex form of the equation, which is given as ( f(x) = a(x - h)^2 + k ), where ( (h, k) ) represents the coordinates of the vertex.

  • The vertex ( (h, k) ) is obtained directly from the equation.
  • The direction of the quadratic function (whether it opens upwards or downwards) depends on the coefficient ( a ) in the vertex form equation:
    • If ( a > 0 ), the parabola opens upwards.
    • If ( a < 0 ), the parabola opens downwards.
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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.

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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