Question

Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest).
f(x) g(x) h(x)
f(x) = 3(x + 4)2 + 1 g(x) = 2x2 − 16x + 15 h(x). graph of 2 times the quantity of x minus 1 squared, minus 3

PLEASE SOMEBODY THIS IS MY LAST QUESTION THEN IM DONE
ILL GIVE BRAINLIEST

Answer 1

The axis of symmetry is the number inside the parenthesis with the x, which is also the x value of the vertex.  And the +1 in f(x) is the y value of the vertex. But the x value has a sign opposite the sign inside the parenthesis with it because of the general form of the equation which is (x-h). So the vertex of f(x) has coordinates of (-4,1) and the axis of symmetry is x= -4.  For g(x), the coordinates of the vertex are found by completing the square. Putting it into vertex form gives you an equation of 2(x-4)^2 - 1 = y with a vertex of (4, -1) so the axis of symmetry is the line x = 4. The last one, h(x), is 2(x - 1)^2 - 3 = y and the vertex has coordinates of (1, -3) and the axis of symmetry is the line x = 1. Putting them in order you have f(x) as the least, h(x) as second, and g(x) as the greatest. If you can't complete the square on a quadrilateral or "read" the vertex form of a quadrilateral, you'll struggle with this.