Question

Ran into some troubles answering this question on that cool old algebra 1, Any help?

ANALYZE Are the following statements sometimes, always, or never true? Justify your argument.



a. The graph of y=x2+k has its vertex at the origin.



b. The graphs of y=ax2 and its reflection across the x-axis are the same width.



c. The graph of f(x)=x2+k , where k≥0 , and the graph of a quadratic function g(x) with vertex at (0, –3) have the same maximum or minimum.

Answer 1

Answer:

(a) sometimes (b) always (c) never true

Step-by-step explanation:

(a) sometimes

for k = 0 the vertex is on origin otherwise on y-axis

(b) always

it's symmetric about y-axis

(c) never true

vertex of f(x) is (0,3) but that of g(x) is given as (0,-3) hence min f(x) at 3 but min/ max of g(x) at -3

note : f(x) has no max