find the vertex, the line of symmetry and the maximum or minimum value of f(x). graph the function. f(x)=-(x+6)^2-2
The vertex is The line of symmetry is x=
The minimum/maximum value of f(x) is?
The value of f(-6) =-2 is maximum or minimum?
and the graph goes up or down.
Thank you
and your thinking is? I will be happy to critique your thinking. It will do you little lasting good if I do these for you.
I believe that x=-2 and the maximum is -2 and the graph goes downward. I did do some excerises with my school work but haven't mastered this.
pls let me know if I have anything right. I appericate you pushing me to find the answer.
"I believe that x=-2 and the maximum is -2 and the graph goes downward...."
How did you find the maximum of f(x)?
Try a tabulation of f(x) from -10 to 0 and see if you spot the maximum at -2 or elsewhere.
You will find that the function was expressed in the form for a reason:
f(x) = A(x-k)² + B
ok the vertex is (-6,2) the line of symmetry is x=-6 and the vlue is max at 2, the graph goes downward. can someone please tell me if I am right. I am trying here.
Could you please verify from your tabulation the value of f(x) when x = -6 (i.e. at the vertex)?
Otherwise the rest are correct.
To find the vertex, line of symmetry, and maximum or minimum value of the function f(x) = -(x + 6)^2 - 2, we can use the standard form of a quadratic equation, f(x) = a(x - h)^2 + k.
Comparing f(x) = -(x + 6)^2 - 2 to the standard form, we can identify that h = -6 (the x-coordinate of the vertex) and k = -2 (the y-coordinate of the vertex).
1. Vertex: The vertex of the parabola is given by the coordinates (h, k), so the vertex of this function is (-6, -2).
2. Line of Symmetry: The line of symmetry is a vertical line that passes through the vertex. Since the vertex is (-6, -2), the line of symmetry will be x = -6.
3. Maximum/Minimum Value: The coefficient 'a' in the standard form determines whether the parabola opens upward (a > 0) or downward (a < 0). In this case, a = -1, which means the parabola opens downward. Therefore, the vertex represents the maximum point of the function. The maximum value of f(x) is the y-coordinate of the vertex, which is -2.
To graph the function, we can plot the vertex (-6, -2) and a few other points to get an idea of the shape of the parabola:
- When x = -7, f(x) = -(-7 + 6)^2 - 2 = -1^2 - 2 = -1 - 2 = -3 -> The point (-7, -3)
- When x = -5, f(x) = -(-5 + 6)^2 - 2 = -(-1)^2 - 2 = -1 - 2 = -3 -> The point (-5, -3)
By plotting these points and recognizing that the parabola opens downward, we can complete the graph accordingly. The graph should be concave down, with the vertex at (-6, -2), and decreasing as we move away from the vertex along the x-axis.