To determine whether the graph of the function [tex]\( v = 2x^2 - 4x + 2 \)[/tex] has a [tex]\( y \)[/tex]-intercept of [tex]\( (0, 2) \)[/tex], we need to evaluate the function at [tex]\( x = 0 \)[/tex].
1. Identify the general form for a quadratic function: The function given is [tex]\( v = 2x^2 - 4x + 2 \)[/tex].
2. Substitute [tex]\( x = 0 \)[/tex] into the function: To find the [tex]\( y \)[/tex]-intercept, we set [tex]\( x \)[/tex] to [tex]\( 0 \)[/tex] because the [tex]\( y \)[/tex]-intercept is where the graph crosses the [tex]\( y \)[/tex]-axis (which occurs when [tex]\( x = 0 \)[/tex]).
3. Calculate the value of [tex]\( v \)[/tex]:
[tex]\[
v = 2(0)^2 - 4(0) + 2
\][/tex]
4. Simplify the expression:
[tex]\[
v = 0 - 0 + 2 = 2
\][/tex]
5. Determine the coordinates of the [tex]\( y \)[/tex]-intercept: When [tex]\( x = 0 \)[/tex], [tex]\( v = 2 \)[/tex]. Therefore, the coordinates of the [tex]\( y \)[/tex]-intercept are [tex]\( (0, 2) \)[/tex].
Thus, the statement "The graph of [tex]\( v = 2x^2 - 4x + 2 \)[/tex] has a [tex]\( y \)[/tex]-intercept of [tex]\( (0, 2) \)[/tex]" is:
A. True
