identify the vertex, axis of symmetry and the dirction of opening for y=-(x-6)^2-5
vertex(6,-5)
Direction is opening down(maximum)
I don't know the axis of symmetry...but I hope this helped:)
Vertex at x = 6, y = -5. That is the largest possible value of y along the curve.
Axis of symmetry is x = 6 vertical line.
Direction of the parabola's opening is down
Oh wait for the axis of symmetry put the vertex form to standard form and then do
-b/2a
For example:
x^2+6x+13 A=1 B=6 C=13
Axis of Symmetry equation x=-b/2a
x=-6/2(1)
x=-3
Sarah,
(x-6)^2 is the same both sides of x = 6. For this problem you do not need
[-b +/- sqrt(b^2-4ac) / 2a
ok well sorry:P
To identify the vertex, axis of symmetry, and direction of opening for the equation y=-(x-6)^2-5, we can use the standard form of a quadratic equation, which is y = a(x-h)^2 + k. In this equation, (h, k) represents the vertex of the parabola.
Comparing the given equation with the standard form, we see that a = -1, h = 6, and k = -5.
1. The vertex: The x-coordinate of the vertex can be found by setting the expression in the parentheses equal to zero and solving for x. So, x - 6 = 0, which gives x = 6. Substituting this value back into the equation y = -(x-6)^2-5, we can find the y-coordinate:
y = -(6-6)^2 - 5
y = -0^2 - 5
y = -5
Therefore, the vertex is (6, -5).
2. The axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex of a parabola. Since the parabola is symmetric, the axis of symmetry is x = 6.
3. The direction of opening: The coefficient "a" in the quadratic equation determines the direction of opening of the parabola. If "a" is positive, the parabola opens upwards, and if "a" is negative, the parabola opens downwards. In our equation, a = -1, so the parabola opens downwards.
To summarize:
- Vertex: (6, -5)
- Axis of symmetry: x = 6
- Direction of opening: Downwards