Questions: The function m is given in three equivalent forms. Which form most quickly reveals the y-intercept? Choose 1 answer: (A) m(x)=2(x+4)^2-8 (B) m(x)=2 x^2+16 x+24 (C) m(x)=2(x+6)(x+2) What is the y-intercept?

Solution Steps

To find the $y$-intercept of a function, we evaluate the function at $x = 0$. The form that most quickly reveals the $y$-intercept is the standard form, which is option (B) $m(x)=2x^2+16x+24$, because the constant term directly gives the $y$-intercept.

We are given three equivalent forms of the function \( m \):

1. \( m(x) = 2(x+4)^{2} - 8 \)
2. \( m(x) = 2x^{2} + 16x + 24 \)
3. \( m(x) = 2(x+6)(x+2) \)

To find the \( y \)-intercept, we need to evaluate the function at \( x = 0 \).

Using the standard form \( m(x) = 2x^{2} + 16x + 24 \), we substitute \( x = 0 \): \[ m(0) = 2(0)^{2} + 16(0) + 24 = 24 \]

The \( y \)-intercept of the function is \( 24 \).

Final Answer