Question
sing the Desmos Graphing Calculator find the y-intercept for the following Quadratic equation
y=0.5x2+2x+1
(3 points)
Responses
(-0.5,0)
(-0.5,0)
(3.4,0)
(3.4,0)
(-2,-1)
(-2,-1)
(0,1)
(0,1)
y=0.5x2+2x+1
(3 points)
Responses
(-0.5,0)
(-0.5,0)
(3.4,0)
(3.4,0)
(-2,-1)
(-2,-1)
(0,1)
(0,1)
Answers
GPT-4o mini
To find the y-intercept of the quadratic equation \( y = 0.5x^2 + 2x + 1 \), you set \( x = 0 \) and solve for \( y \).
Substituting \( x = 0 \) into the equation:
\[
y = 0.5(0)^2 + 2(0) + 1
\]
This simplifies to:
\[
y = 0 + 0 + 1
\]
Thus, \( y = 1 \).
The y-intercept is the point where the graph intersects the y-axis, which corresponds to the point \( (0, y) \). Therefore, the y-intercept for the equation \( y = 0.5x^2 + 2x + 1 \) is:
\[
(0, 1)
\]
The correct response is **(0, 1)**.
Substituting \( x = 0 \) into the equation:
\[
y = 0.5(0)^2 + 2(0) + 1
\]
This simplifies to:
\[
y = 0 + 0 + 1
\]
Thus, \( y = 1 \).
The y-intercept is the point where the graph intersects the y-axis, which corresponds to the point \( (0, y) \). Therefore, the y-intercept for the equation \( y = 0.5x^2 + 2x + 1 \) is:
\[
(0, 1)
\]
The correct response is **(0, 1)**.