The correct statements are 1,2 and 3.
"The vertex of function g is 4 units to the left of the vertex of function f."
"The vertex of function g is 2 units below the vertex of function f."
"Function opens in the opposite direction of function f."
What is the quadratic function?
In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree.
Here we have the two quadratic functions:
f(x) = 4(x - 3)²+ 6
g(x) = -2(x + 1)²+ 4
The x-value of the vertex is the value of x such that the first term becomes equal to zero, so for f(x) the vertex is at x = 3, and the y-value of the vertex is:
f(3) = 0 + 6 = 6
So the vertex is (3, 6)
For g(x) we can see that the vertex is at x = -1, and:
g(-1) = 0 + 4=4
So the vertex is at (-1, 4)
Also, you can see that for g(x) and f(x) the leading coefficients are of different signs. Meaning that f(x) opens upwards and g(x) opens downwards.
Hence, options 1,2 and three are correct answers.
To learn more about the quadratic functions visit:
https://brainly.com/question/27918223.
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