Question

question 8
0.5 pts
in the equation $y = 3|x - 6| + 1$, what does the 6 do to the graph of the parent function?

• moves down 6
• moves right 6
• shrinks by a factor of 6
• flips over the axis

question 9
0.5 pts
in the equation $y = -3x^2 + 1$, what does the negative in front of the 3 do to the graph of the parent function?

• flips over the x - axis
• moves down 2 units

Explanation:

Question 8

The parent function of \( y = 3|x - 6| + 1 \) is \( y = |x| \). For absolute - value functions of the form \( y=a|x - h|+k \), the value of \( h \) (here \( h = 6 \)) represents a horizontal shift. If \( h>0 \), the graph shifts to the right by \( h \) units. In the equation \( y = 3|x - 6|+1 \), the \( 6 \) is part of the \( x - 6 \) term, so it moves the graph of the parent function \( y = |x| \) to the right by 6 units. The "moves down 6" is incorrect as vertical shifts are related to the constant term at the end. "Shrinks by a factor of 6" is incorrect as the coefficient related to shrinking or stretching is the coefficient of the absolute - value term (here 3), not the number inside the absolute - value. "Flips over the axis" is incorrect as there is no negative sign affecting the reflection here.

The parent function of \( y=-3x^{2}+1 \) is \( y = x^{2} \). For quadratic functions of the form \( y = ax^{2}+bx + c \), the sign of \( a \) determines the direction of the parabola. If \( a>0 \), the parabola opens upwards, and if \( a < 0 \), the parabola opens downwards. A negative sign in front of the coefficient of \( x^{2} \) (here the coefficient of \( x^{2} \) is - 3) reflects the graph of the parent function \( y=x^{2} \) over the \( x \) - axis. The option about moving down 2 units is incorrect as the vertical shift is related to the constant term (here 1), and the negative sign is not related to vertical movement but to reflection.

Answer:

B. Moves right 6

Question 9