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If the equation $y=2(1.5)^{x}$ is graphed in the $xy$ -plane, what are the coordinates of its y-intercept? $\newline$ Choose $1$ answer: $\newline$ (A) $(0,0)$ $\newline$ (B) $(0,1.5)$ $\newline$ (C) $(0,2)$ $\newline$ (D) $(0,3)$

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. If the equation

y=2(1.5)^{x}

is graphed in the

xy

-plane, what are the coordinates of its y-intercept?

\newline

Choose

1

answer:

\newline

(A)

(0,0)

\newline

(B)

(0,1.5)

\newline

(C)

(0,2)

\newline

(D)

(0,3)

Determine y-intercept: To find the y-intercept of the equation $y = 2(1.5)^x$ , we need to determine the value of $y$ when $x = 0$ . The y-intercept occurs where the graph of the equation crosses the y-axis, which is at $x = 0$ .
Substitute $x=0$ : Substitute $x = 0$ into the equation to find the $y$ -coordinate of the $y$ -intercept. $\newline$ $y = 2(1.5)^0$ $\newline$ Since any number to the power of $0$ is $1$ , we have: $\newline$ $y = 2(1)$
Simplify equation: Simplify the equation to find the value of $y$ . $y = 2 \times 1$ $y = 2$
Find coordinates: The coordinates of the y-intercept are $(0, y)$ . Since we found $y = 2$ when $x = 0$ , the coordinates of the y-intercept are $(0, 2)$ .

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