Answer:
Vertex: -3, 0
y-intercept: 9
x-intercept: -3
Step-by-step explanation:
Convert into vertex form after factoring:
(x + 3)^2 + 0
Reorder your equation so it matches that of a parabola:
y = (x + 3)^2
Use the vertex form, y = a(x−h)^2 + k, to determine the values of a, h, and k.
a = 1
h = −3
k = 0
Now you have your vertex: (-3, 0)
To graph, use the intercepts.
To find the y-intercept, your x has to equal 0.
y = 0^2 + 6(0) + 9
y = 9
To find the x-intercept, your y has to equal 0.
x^2 + 6x + 9 = 0
Then use the quadratic formula to solve:
b ± √b^2 - 4(a x c) /2a
Replace a with 1, b with 6 and c with 9:
-6 ± √6^2 - 4(1 x 9) /2(1)
Solve:
-6 ± √36 - 36 /2(1)
-6 + 0 /2
-6/2
x = -3
