Question

test information
description
instructions
multiple attempts this test allows multiple attempts.
force completion this test can be saved and resumed later.
your answers are saved automatically.

question completion status:

moving to another question will save this response.

question 9

let ( y = f(x) ) be a quadratic function given by ( f(x) = ax^2 + bx + c ).

this function can have exactly one y-intercept.

○ true
○ false

moving to another question will save this response.

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a function \(y = f(x)\) is found by setting \(x = 0\) and solving for \(y\). For the quadratic function \(f(x)=ax^{2}+bx + c\), when \(x = 0\), we have \(f(0)=a(0)^{2}+b(0)+c=c\).

Step2: Analyze the result

The value of \(f(0)\) is \(c\), which is a single value (since \(a\), \(b\), and \(c\) are constants for a given quadratic function). So, regardless of the values of \(a\) and \(b\) (as long as \(a
eq0\) for it to be quadratic), when \(x = 0\), there is exactly one value of \(y\) (which is \(c\)). So the function \(y = f(x)=ax^{2}+bx + c\) has exactly one y - intercept.

Answer:

True