How do you graph the function, label the vertex, axis of symmetry, and x-intercepts. #y=x^2-16x + 63#?

Answer 1
#y=x^2-16x+63#
Has a y-intercept at #y=63# as determined by setting #x=0# (and, yes; I know this wasn't asked for but it might help in graphing)
Since #(x^2-16x+63)# can be factored as #(x-7)(x-9)#, the x-intercepts are at #7# and #9#
The vertex occurs at the point where #y'=0# #y'=2x-16= 0 rarr x=8# (This could also be determined as the mid x coordinate between the two x-intercepts). At #x=8# #y=8^2-16(8)+63 = 0# So the vertex is at #(8,0)#
This equation is that of a standard parabola so the axis of symmetry is the vertical line through the vertex: #x=8# graph{x^2-16x+63 [-5.47, 22.99, -2, 12.25]}

I'm not very good at drawing smooth curves so I've used an external tool; the labeling is up to you)

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Answer 2

To graph the function ( y = x^2 - 16x + 63 ):

  1. Find the vertex using the formula ( x = -\frac{b}{2a} ).
  2. Calculate the y-coordinate of the vertex by substituting the x-coordinate into the function.
  3. Determine the axis of symmetry, which is the vertical line passing through the vertex.
  4. Find the x-intercepts by setting ( y = 0 ) and solving the quadratic equation.
  5. Plot the vertex, axis of symmetry, and x-intercepts on the coordinate plane.
  6. Sketch the parabola passing through these points.
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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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