What are the points of intersection of #y=-2x^2-5x+3# and #y=-2x+3#?

2 Answers
Sep 5, 2016

#(0,3), and, (-3/2,6)#.

Explanation:

To find the pts. of intersection of these two curves, we have to solve

their eqns.

#y=-2x^2-5x+3, and, y=-2x+3#

#:. -2x+3=-2x^2-5x+3, or, 2x^2+3x=0#

#:. x(2x+3)=0#

#:. x=0, x=-3/2#

#:. y=-2x+3=3, y=6#

These roots satisfy the given eqns.

Hence, the desired pts. of int. are #(0,3), and, (-3/2,6)#.

Sep 5, 2016

At points #(0, 3); (-1.5, 6) # the two curves intersets

Explanation:

Given -

#y=-2x^2-5x+3#
#y=-2x+3#

To find the intersection point of these two curves, set -

#-2x^2-5x+3=-2x+3#

Solve it for #x#

You will get at what values of #x# these two intersect

#-2x^2-5x+3+2x-3=0#
#-2x^2-3x=0#
#x(-2x-3)=0#
#x=0#
#x=3/(-2)=-1.5#

When #x#takes the values 0 and - 1.5 the two intersects

To find the point of intersection, we must know the Y-cordinate

Substitute #x# in any one of the equations.

#y=-2(0)+3#
#y=3#

At #(0, 3) # the two curves intersets

#y=-2(1.5)+3=3+3=6#

At #(-1.5, 6)# the two curves intersects

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