Question

I need help please could someone try to help me on solving quadratic equations by graphing step by step w squared +6w +9=0

Answer 1

or atleast some help plz

Answer 2

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