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

y-intercept
=(0,◻)

The function $m$ is given in three equivalent forms. $\newline$ Which form most quickly reveals the $y$ -intercept? $\newline$ Choose $1$ answer: $\newline$ (A) $m(x)=2 x^{2}+16 x+24$ $\newline$ (B) $m(x)=2(x+4)^{2}-8$ $\newline$ (C) $m(x)=2(x+6)(x+2$ ) $\newline$ What is the $y$ -intercept? $\newline$ $y$ -intercept $=(0, \square)$

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Solve a quadratic equation using the zero product property

Full solution

Q. The function

m

is given in three equivalent forms.

\newline

Which form most quickly reveals the

y

-intercept?

\newline

Choose

1

answer:

\newline

(A)

m(x)=2 x^{2}+16 x+24

\newline

(B)

m(x)=2(x+4)^{2}-8

\newline

(C)

m(x)=2(x+6)(x+2

)

\newline

What is the

y

-intercept?

\newline

y

-intercept

=(0, \square)

Definition: The $y$ -intercept of a function is the point where the graph of the function crosses the $y$ -axis. This occurs when the input $x$ is equal to $0$ . To find the $y$ -intercept, we need to evaluate the function at $x = 0$ .
Evaluate Option (A): Let's evaluate option (A) $m(x) = 2x^2 + 16x + 24$ at $x = 0$ . $\newline$ $m(0) = 2(0)^2 + 16(0) + 24 = 0 + 0 + 24 = 24$ $\newline$ The y-intercept for option (A) is $(0, 24)$ .
Evaluate Option (B): Now let's evaluate option (B) $m(x) = 2(x + 4)^2 - 8$ at $x = 0$ .
$m(0) = 2(0 + 4)^2 - 8 = 2(4)^2 - 8 = 2(16) - 8 = 32 - 8 = 24$
The y-intercept for option (B) is also $(0, 24)$ .
Evaluate Option (C): Finally, let's evaluate option (C) $m(x) = 2(x + 6)(x + 2)$ at $x = 0$ . $\newline$ $m(0) = 2(0 + 6)(0 + 2) = 2(6)(2) = 2 \times 12 = 24$ $\newline$ The y-intercept for option (C) is $(0, 24)$ as well.
Comparison: All three options give us the same y-intercept, $(0, 24)$ . However, the question asks which form most quickly reveals the y-intercept. The standard form (A) $m(x) = 2x^2 + 16x + 24$ directly shows the constant term $+24$ , which is the y-intercept when $x = 0$ . Therefore, option (A) most quickly reveals the y-intercept without any additional calculations or transformations.

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