The 2nd question has a fraction and I think this is confusing me on this one
f(x)=1/5(x+7)^2+7
I need to find the vertex line of symmetry max/min and is the value f(-7)=7 a minimum or a maximum?
You typed that so I am not sure what you mean.
y = (1/5) (x+7)^2 + 7
or
y = 1/[5(x+7)^2] + 7
I will assume the first.
then
(y-7) = (1/5)(x+7)^2
when x = -7 (the axis of symmetry), the right is zero so y = 7
as x gets big or very negative, y gets big so parabola faces up (holds water).
Therefore the vertex at (-7,7) is a minimum
Thanks so much I just looked at my answers and I realized I had gotten the right answers after all. Many thanks
To find the vertex, line of symmetry, and whether the value f(-7) = 7 is a minimum or maximum, we can use the graphing technique or algebraic approach.
Let's start with the algebraic approach:
1. Finding the vertex:
In this problem, the equation is in vertex form: f(x) = a(x-h)^2 + k, where (h, k) represents the vertex.
Comparing the given equation f(x) = 1/5(x+7)^2 + 7 with the vertex form equation, we can see that h = -7 and k = 7.
So, the vertex is at (-7, 7).
2. Determining the line of symmetry:
The line of symmetry is a vertical line that passes through the vertex.
In this case, the line of symmetry is x = -7.
3. Identifying whether the value f(-7) = 7 is a minimum or maximum:
To determine if it is a minimum or maximum, we need to examine the coefficient 'a' in the vertex form equation.
Since the coefficient of the squared term is positive (1/5), the parabola opens upward, and the vertex represents the minimum point.
Therefore, the vertex is (-7, 7), the line of symmetry is x = -7, and the value f(-7) = 7 represents the minimum point on the graph.
If you want to visualize the graph, you can plot the vertex (-7, 7) and a few other points to get an idea of the parabola's shape.