MHB Can Plugging in (x/2) or (x - 1/2) Determine Real Zeros in a Quadratic Equation?

[mathland]

I can replace f(x) with x - x^2. Should I plug (x/2) into f(x)? How about (x - 1/2) into f(x)? I need the set up.

 

[Greg]

Note the range of $f(x)$. A and B are vertical shifts, C and D are horizontal shifts. Which one of the given shifts would result in the graph of $f(x)$ not crossing the $x-\text{axis}$?

 

[mathland]

Note the range of $f(x)$. A and B are vertical shifts, C and D are horizontal shifts. Which one of the given shifts would result in the graph of $f(x)$ not crossing the $x-\text{axis}$?

Let y = the function.

y = x - x^2 - 1/2 does not cross the line y = 0.

 

[Greg]

Note the concavity of $f(x)$. What does that tell you about lowering the graph of $f(x)$? (the line $y=0$ does not concern us presently).

 

[skeeter]

write each quadratic in standard form, $ax^2+bx+c$ ... check each discriminant, $D = b^2-4ac$

you know what the discriminant can tell you about the nature of zeros, right?