Questions: A function in the form of f(x)=a x^2+b x+c when a ≠ 0 is a quadratic function. Select one: True False

Transcript text: A function in the form of $f(x)=a x^{2}+b x+c$ when $a \neq 0$ is a quadratic function. Select one: True False

Solution

Solution Steps

To determine if the statement is true or false, we need to check if the given function form $ f(x) = ax^2 + bx + c $ with $ a \neq 0 $ is indeed a quadratic function. A quadratic function is defined as a polynomial of degree 2, which is satisfied by the given form since the highest power of $ x $ is 2 and $ a \neq 0 $ ensures it is not a linear function.

Step 1: Identify the Function Form

The function is given in the form $ f(x) = ax^2 + bx + c $. For this to be classified as a quadratic function, the coefficient $ a $ must be non-zero, i.e., $ a \neq 0 $.

Step 2: Check the Condition

In the example provided, we have $ a = 1 $, $ b = 2 $, and $ c = 3 $. Since $ a = 1 $ satisfies the condition $ a \neq 0 $, the function is indeed a quadratic function.

Step 3: Conclusion

Since the condition for being a quadratic function is met, we conclude that the statement is true.