How do you graph #F(x)=x^2-6x+8#?

Answer 1

See answer below

Given: #f(x) = x^2 -6x + 8#

This function is a quadratic - a graph of a parabola.

Factor and let #f(x) = 0# to find the x-intercepts :
#x^2 -6x + 8 = (x - 2)(x - 4) = 0#

#x - 2 = 0 " "=> x = 2; " "x - 4 = 0 " "=> x = 4

#x#-intercepts: " "(2, 0), (4, 0)#
Find the y-intercept let #x = 0#:
#f(0) = 0^2 -6*0 + 8 = 0#
#y#-intercept: " "(0, 8)#
Find the vertex . When the equation is in #Ax^2 + Bx + C = 0#,
the vertex is #(-B/(2A), f(-B/(2A)))#
#-B/(2A) = 6/2 = 3#
#f(3) = 3^2 -6*3 + 8 = -1#
vertex: #(3, -1)#
Plot a couple of other points using point-plotting. Since #x# is the independent variable, you can select any #x# and calculate the corresponding #y#:
#ul(" "x" "|" "y" ")# #" "1" "|" "3" "# #" "5" "|" "3" "# #" "6" "|" "8" "#

graph{x^2 -6x + 8 [-5, 10, -2, 10]}

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Answer 2

To graph the function ( f(x) = x^2 - 6x + 8 ), you can follow these steps:

  1. Determine the vertex of the parabola using the formula ( x = \frac{-b}{2a} ), where ( a ) is the coefficient of ( x^2 ) (in this case, ( a = 1 )) and ( b ) is the coefficient of ( x ) (in this case, ( b = -6 )).
  2. Once you have the ( x )-coordinate of the vertex, substitute it into the function to find the corresponding ( y )-coordinate.
  3. Plot the vertex on the coordinate plane.
  4. Find at least two additional points on either side of the vertex by choosing values of ( x ) and substituting them into the function to find the corresponding ( y )-values.
  5. Plot these points on the graph.
  6. Draw a smooth curve passing through all the plotted points to represent the graph of the function.

Alternatively, you can also use other methods such as completing the square or factoring to graph the function.

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Answer 3

To graph the function ( F(x) = x^2 - 6x + 8 ), follow these steps:

  1. Identify the vertex of the parabola using the formula ( x = -\frac{b}{2a} ), where ( a ) and ( b ) are the coefficients of the quadratic equation in the form ( ax^2 + bx + c ).
  2. Calculate the ( y )-coordinate of the vertex by substituting the ( x )-value from step 1 into the equation ( F(x) ).
  3. Determine whether the parabola opens upwards or downwards based on the sign of the coefficient ( a ).
  4. Plot the vertex on the coordinate plane.
  5. Choose additional points on either side of the vertex to plot on the graph.
  6. Use symmetry to plot corresponding points on the opposite side of the vertex.
  7. Connect the plotted points to sketch the graph of the quadratic function.
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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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