anonymous
  • anonymous
I need help please could someone try to help me on solving quadratic equations by graphing step by step w squared +6w +9=0
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
or atleast some help plz
dumbcow
  • dumbcow
ok to graph this you need to first find vertex (max or min) Vertex: every quadratic is in the form ax^2+bx+c the x-value of vertex (known as line of symmetry) is -b/2a For w^2+6w+9 our coefficients are a=1 b=6 c=9 -> x = (-6)/2(1) = -3 to get y-value substitute -3 back into equation for w y = (-3)^2 +6*(-3) +9 = 9 -18 +9 = 0 vertex = (-3,0) plot this point on the graph To get more points pick w values to plug back in w = 0 -> y = 0^2 + 6(0) +9 = 9 point = (0,9) plot this point on graph because quadratic graphs are symmetric then if we go over 3 from the vertex in the other direction, w = -6 y will also be 9 y = (-6)^2 + (-6)(6) +9 = 36-36+9 = 9 plot the point(-6,9) now draw a line connecting your points theres your graph Solving: so to solve w^2+6w+9 = 0 we see that y=0 which corresponds to the x-axis look on graph and find points where line is touching the x-axis you should notice only one point our vertex(-3,0) so answer is -3

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