QuestionWhat is the axis of symmetry of the parabola $y=5(x-6)^{2}-7 ?$

Studdy Solution

STEP 1

1. The equation of the parabola is given in vertex form.
2. The vertex form of a parabola is $y = a(x-h)^2 + k$ .
3. The axis of symmetry for a parabola in vertex form is the vertical line $x = h$ .

STEP 2

1. Identify the vertex form components.
2. Determine the axis of symmetry.

STEP 3

Identify the components of the vertex form from the given equation $y = 5(x-6)^2 - 7$ .
The vertex form of a parabola is $y = a(x-h)^2 + k$ .
In the given equation: - $a = 5$ - $h = 6$ - $k = -7$

STEP 4

Determine the axis of symmetry.
The axis of symmetry for a parabola in vertex form $y = a(x-h)^2 + k$ is the vertical line $x = h$ .
Thus, the axis of symmetry is:
$x = 6$
The axis of symmetry of the parabola is:
$\boxed{x = 6}$

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