Question

a quadratic function $f(x)$ is hidden from view. you must find the $y$-intercept(s) of $f(x)$ and write the answer(s) in the form $(x, y)$. choose the form of the quadratic function $f(x)$ that you would like to see in order to answer the question most efficiently.

form: select a form

answer attempt 1 out of 2
there are no $y$-intercepts

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \( f(x) \) is the point where \( x = 0 \). So we need to find \( f(0) \).

Step2: Choose efficient quadratic form

The standard form of a quadratic function is \( f(x)=ax^{2}+bx + c \), where \( c \) is the y - intercept (since when \( x = 0 \), \( f(0)=a(0)^{2}+b(0)+c=c \), so the y - intercept is \( (0,c) \)). So the most efficient form to find the y - intercept is the standard form \( f(x)=ax^{2}+bx + c \).

Step3: Find y - intercept from standard form

Once we have the function in standard form \( f(x)=ax^{2}+bx + c \), we substitute \( x = 0 \). Then \( f(0)=a(0)^{2}+b(0)+c=c \). So the y - intercept is \( (0,c) \).

Answer:

To find the y - intercept of a quadratic function \( f(x) \) most efficiently, we should choose the standard form \( f(x)=ax^{2}+bx + c \). The y - intercept is found by substituting \( x = 0 \) into the function. For a quadratic function in standard form, \( f(0)=c \), so the y - intercept is \( (0,c) \). (Note: Since the problem's form selection and answer dropdown are not fully populated with the function details, but the method is as above. If we had the function in standard form \( f(x)=ax^{2}+bx + c \), the y - intercept would be \( (0,c) \).)