Describe the graph.

Question

Describe the graph of f(x) = a(x - h)^2 + k when a = 0. Is the graph the same as that of g(x) = ax^2 + bx + c when a = 0? Explain.

Answer 1

If a= 0, this is no longer a formula for a parabola,

it is the horizontal line y = k.

 

Second question is a no, unless b= 0 as well.  

The equation y = bx + c, when b ≠ 0, has a slope makes it diverge from the horizontal.

Answer 2

Let's expand the function when a=0.

 

f(x) = a(x - h)(x - h) + k

 

f(x) = a(x² - 2xh + h²) + k

 

f(x) = ax² - 2axh + 2ah² + k

 

f(x) = k

 

 

This indicates that when a=0, a horizontal line passes though the position where the vertex of the original equation would be located at.  Because the graph is a line, it is not the same as that of g(x), which is a parabola.