Question

what statement is true?
a zero and a root mean different things.
zeros only exist for quadratic functions
a zero is where the graph crosses the y - axis
a root is an x - value that makes the function equal zero

Explanation:

• Analyze each option:
• Option 1: "A zero and a root mean different things" is false. In the context of functions, a zero (of a function) and a root (of an equation) are essentially the same concept—an x - value that makes the function equal to zero.
• Option 2: "Zeros only exist for quadratic functions" is false. Zeros (or roots) exist for many types of functions, such as linear functions ($y = mx + b$ has a zero when $mx + b=0$), cubic functions, exponential functions (in some cases), etc.
• Option 3: "A zero is where the graph crosses the y - axis" is false. A zero of a function is where the graph crosses the x - axis (where $y = 0$), and the y - intercept is where the graph crosses the y - axis (where $x = 0$).
• Option 4: "A root is an x - value that makes the function equal zero" is true. By definition, for a function $y = f(x)$, a root (or zero) of the function is an $x$ - value such that $f(x)=0$.

Answer:

D. A root is an x - value that makes the function equal zero