Math  /  Geometry

QuestionFind the axis of symmetry of the parabola defined by the equation (y+6)2=40(x+6)(y+6)^{2}=40(x+6).

Studdy Solution

STEP 1

1. The equation (y+6)2=40(x+6)(y+6)^2 = 40(x+6) represents a parabola.
2. The parabola is oriented horizontally, as the yy term is squared.

STEP 2

1. Identify the standard form of a horizontally oriented parabola.
2. Rewrite the given equation in standard form.
3. Determine the axis of symmetry from the standard form.

STEP 3

Identify the standard form of a horizontally oriented parabola:
The standard form of a horizontally oriented parabola is:
(yk)2=4p(xh) (y - k)^2 = 4p(x - h)
where (h,k)(h, k) is the vertex of the parabola.

STEP 4

Rewrite the given equation in standard form:
Given equation: (y+6)2=40(x+6)(y+6)^2 = 40(x+6)
Compare with the standard form (yk)2=4p(xh)(y - k)^2 = 4p(x - h):
- Here, k=6k = -6, h=6h = -6, and 4p=404p = 40.

STEP 5

Determine the axis of symmetry from the standard form:
For a horizontally oriented parabola, the axis of symmetry is the horizontal line y=ky = k.
Since k=6k = -6, the axis of symmetry is:
y=6 y = -6
The axis of symmetry of the parabola is:
y=6 \boxed{y = -6}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord