Question

Mon Core Algebra I A-CR

The graph of f(x) = (x - h\ + k contains the points (-6, -2)
and (0, -2). The graph has a vertex at (h, -5). Describe
how to find the value of h. Then, explain how this value
translates the graph of the parent function.

Answer 1

Sample Response: The absolute value function is symmetric. Since the points (–6, –2) and (0, –2) have the same output, the points are the same distance from the line of symmetry. Between –6 and 0 is the value of –3. So, the vertex must have an x-coordinate of –3, which is the value of h. This would translate the graph of the parent function 3 units to the left.

Answer 2

h = -3

The value h = -3 translates the graph of the parent function
`y=x^2` 3 units to the left.

Explanation:

The graph of
`f(x)=(x-h)^2+k` contains the points (-6, -2) and (0, -2).

This is the equation of parabola in vertex form, where
`(h,k)` are the coordinates of the vertex.

If the graph has a vertex at
`(h,-5),` then
`k=-5.`

So, the equation of the parabola is

`f(x)=(x-h)^2-5`

If the graph passes through the points (0,-2) and (-6,-2) (these two points lie on the same horizontal line y = -2), then the parabola vertical line of symmetry divides the segment between these points into two congruent segments. Hence, the equation of the line of symmetry is

`x=(0+(-6))/(2)=-3`

The vertex lies on the line of symmetry, so its x-coordinate is -3. Thus, (-3,-5) is the vertex.

The value h = -3 translates the graph of the parent function
`y=x^2` 3 units to the left.