What are the intercepts of #y=2(x-3)(x+5)#?

2 Answers
Feb 7, 2018

Answer:

See below...

Explanation:

We know that the x intercepts of any quadratic is where the roots are #=# to #0#

#therefore# using #2(x-3)(x+5)=0#

#therefore# #x-3 = 0#
#=># #x=3#

#therefore x+5=0#
#=> x=-5#

As the roots occur at #y=0#, we get the coordinates of intersection on the x axis are #(3,0) , (-5,0)#

Now we need to work out the y intercept (the point where it crosses the y axis). This will always occur at #x=0# always giving coordinates in the form #(0,y)#

#therefore# subbing #x=0# in the equation, we get.

#2(0-3)(0+5)#
#2(-3)(5)=-30#

#therefore# the y intercept is at #(0,-30)#

Feb 7, 2018

Answer:

#y=-30" and "x=-5,3#

Explanation:

#"to find the intercepts, that is where the graph crosses"#
#"the x and y axes"#

#• " let x = 0, in the equation for y-intercept"#

#• " let y = 0, in the equation for x-intercepts"#

#x=0toy=2(-3)(5)=-30larrcolor(red)"y-intercept"#

#y=0to2(x-3)(x+5)=0#

#"equate each factor to zero and solve for x"#

#x-3=0rArrx=3larrcolor(red)"x-intercept"#

#x+5=0rArrx=-5larrcolor(red)"x-intercept"#
graph{2(x-3)(x+5) [-10, 10, -5, 5]}