How do you identify the important parts of #y= -7x^2# to graph it?

Answer 1

The axis of symmetry is #x=0#/
The vertex is #(0,0)#.

#y=-7x^2# is a quadratic equation in standard form #ax^2+bx+c#, where #a=-7, b=0, and c=0#.

Axis of Symmetry: an imaginary vertical line the divides the parabola into two equal halves.

Formula for axis of symmetry: #x=(-b)/(2a)#
Since #b=0#, the axis of symmetry is #x=0#.
Vertex: The maximum or minimum point #(x,y)# of a parabola. Since the coefficient of #a# is negative, this parabola opens downward and the vertex is the maximum point. The #x# value for the vertex is the value for the axis of symmetry, where #x=0#.
To find the #y# value of the vertex, we substitute #0# for #x# in the equation and solve for #y#.
#y=-7x^2=#
#y=-7(0)^2=0#
The vertex is #(0,0)#.

Determine a few points on both sides of the axis of symmetry.

#x=-2,# #y=-28# #x=-1,# #y=-7# #x=0,# #y=0# (vertex) #x=1,# #y=-7# #x=2,# #y=-28#

Plot the points and sketch a curved parabola through the points. Do not connect the dots.

graph{y=-7x^2 [-14.49, 17.53, -11.08, 4.94]}

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Answer 2

To graph the equation y = -7x^2, identify the following key components:

  1. The coefficient of x^2, which determines the direction and degree of the parabola's opening.
  2. The vertex, which is the highest or lowest point on the graph.
  3. The axis of symmetry, which is a vertical line passing through the vertex, dividing the parabola into two symmetrical halves.
  4. The y-intercept, which is where the graph intersects the y-axis.
  5. Additional points on the graph can be found by selecting x-values and substituting them into the equation to find corresponding y-values.
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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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