Find the vertex and axis of symmetry of the graph of a function.
f(x)=x^2+6x+16
f(x) = x^2+6x+16
= x^2 +6x +9 +3
= (x+3)^2 +3
The vertex (lowest point) is x= -3, y = 3. That is because (x+3)^2 can never ne negative.
It is symmetrical about the x=-3 vertical line.
f(x) = x^2 + 6x + 16.
h = Xv = -b / 2a = -6 / 2 = -3,
Substitute -3 for x in the given Eq:
k = Yv = (-3)^2 + 6*-3 16,
k = 9 - 18 + 16 = 25 - 18 = 7,
V(h , k) = V(-3 , 7).
Axis: h = Xv = -3. = A vertical line
where x isconstant at -3 for all values of y.
To find the vertex and axis of symmetry of the graph of the function f(x) = x^2 + 6x + 16, we can use the formula for the vertex of a quadratic function:
The vertex formula for a quadratic function f(x) = ax^2 + bx + c is given by:
x = -b/2a
y = f(x)
In our case, a = 1, b = 6, and c = 16.
1. Find x-coordinate of the vertex:
x = -b/2a = -(6)/(2*1) = -6/2 = -3
2. Substitute x = -3 into the original function to find y-coordinate of the vertex:
f(-3) = (-3)^2 + 6(-3) + 16
= 9 - 18 + 16
= 7
So, the vertex is (-3, 7).
The axis of symmetry is a vertical line that passes through the vertex. The equation of the axis of symmetry can be found by taking the x-coordinate of the vertex.
Axis of symmetry: x = -3
To find the vertex and axis of symmetry of the graph of a function, you can use the formula -b/2a, where the equation of the function is in the form ax^2 + bx + c.
For the given function f(x) = x^2 + 6x + 16:
1) Identify the values of a, b, and c from the equation. In this case, a = 1, b = 6, and c = 16.
2) Use the formula -b/2a to find the x-coordinate of the vertex. By plugging in these values, we get:
x = -6 / (2 * 1) = -6 / 2 = -3.
3) Substituting this x-coordinate back into the original equation, we can find the y-coordinate of the vertex. By plugging in x = -3, we get:
f(-3) = (-3)^2 + 6(-3) + 16 = 9 - 18 + 16 = 7.
Therefore, the vertex of the graph is (-3, 7).
4) The axis of symmetry is a vertical line that passes through the vertex. In this case, the axis of symmetry is the vertical line x = -3.
So, the vertex of the graph is (-3, 7), and the axis of symmetry is x = -3.