How do you graph the quadratic function and identify the vertex and axis of symmetry for #y=-(x-2)^2-1#?

Answer 1

#(2,-1),x=2#

The equation of a parabola in #color(blue)"vertex form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))# where (h ,k) are the coordinates of the vertex and a is a constant.
#y=-(x-2)^2-1" is in this form"#
and by comparison #h=2" and " k=-1#
#rArr"vertex "=(2,-1)#
Since the #color(blue)"value of a is negative"#
#"That is " color(red)(-)(x-2)^2#
Then the parabola opens down vertically #color(red)(nnn#
The axis of symmetry goes through the vertex and therefore has equation #color(magenta)"x=2"#
#color(blue)"Intercepts"#
#x=0toy=-(0-2)^2-1=-4-1=-5#
#rArry=-5larrcolor(red)"y-intercept"#
#y=0to-(x-2)^2-1=0to(x-2)^2=-1#

This has no real solutions hence there are no x-intercepts.

Knowing the ' shape' of the parabola, the vertex and the y-intercept enables the graph to be sketched. graph{-(x-2)^2-1 [-10, 10, -5, 5]}

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Answer 2

To graph the quadratic function ( y = -(x-2)^2-1 ) and identify the vertex and axis of symmetry:

  1. Plot the vertex at the point (2, -1).
  2. Since the coefficient of ( x^2 ) is negative, the parabola opens downwards.
  3. The axis of symmetry is the vertical line passing through the vertex, which is ( x = 2 ).
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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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