For our quadratic function, we will see that the vertex is the point (2, 6), and the axis of symmetry is x = 2.
For a general quadratic function:
f(x) = a*x^2 + b*x + c
The vertex has the x-value:
x = -b/(2a).
Then for our function:
f(x) = 3*(x - 2)^2 + 4
First, we should expand it, so we get:
f(x) = 3*(x^2 - 4x + 4) + 4
f(x) = 3x^2 - 12x + 18
Then the x-value of the vertex is:
x = 12/(2*3) = 2
To get the y-value of the vertex, we just evaluate the function in the x-value of the vertex, we will get:
f(2) = 3*2^2 - 12*2 + 18 = 3*4 - 24 + 18 = 12 - 24 + 18 = 6
Then the vertex is (2, 6).
And the axis of symmetry will be a vertical line that cuts the parabola in two halves, such that this axis passes through the vertex, then the vertical line must be:
x = 2.
If you want to learn more about quadratic equations, you can read:
https://brainly.com/question/1214333
