Question

Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.

f(x)=3(x+4)²+1

Answer 1

Explanation:

the axis of symmetry for a regular parabola (opens up or down) is a line parallel to the y-axis (vertical) going through the vertex of the parabola.

the standard form of a parabola is

y = a(x - h)² + k

with (h, k) being the vertex.

so, we see for f(x) the vertex is (-4, 1).

the axis of symmetry uses the x coordinate of the vertex and is

x = -4

for h(x) we see in the graphic that the vertex is (1, -3).

so, the axis of symmetry is

x = 1

FYI - based on what we see : vertex is (1, -3), h(0) = -1 the function here would be

h(x) = 2(x - 1)² - 3