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

1 Answer
Meave60
Oct 9, 2015

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

Explanation:

#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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