How do you graph the parabola #y= (x + 3)^2 - 2# using vertex, intercepts and additional points?

1 Answer
Jul 10, 2016

Refer explanation section

Explanation:

The given quadratic equation is in the vertex form

#y=(x-3)^2-2#

Hence the vertex is #(3, -2)#

#(3, -2)#This is one of the points on the curve.

#x=-3# is the minimum point on the curve. Hence to graph the curve, we take two point to the left of #x=3# and two point to its right.

Right side points -

At #x=5; y=(5-3)^2-2=4-2=2#

#(5,2)#

At #x=4; y=(4-3)^2-2=1-2=-1#

#(-4,-1)#

#(3, -2)#

Left side points.

At #x=2; y=(2-3)^2-2=1-2=-1#

#(-2, -1)#

At #x=1; y=(1-3)^2-2=4-2=2#

#(-1,2)#

Plot the points
#(5, 2), (4, -1), (3, -2), (2, 1), (-1, 2)#

Table developed in Excel for the equation #y=(x-3)^2-2#

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You will get the graph.

Graph developed in Excel

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