Question

algebra 2a semester online practice
complete this assessment to review what youve learned. it will not count toward your grade.
which of the following equations has the same minimum as the absolute value parent function? (1 point)
○ $y = x^2$
○ $y = x$
○ $y = -x$
○ $y = -x^2$

Explanation:

Step1: Analyze absolute value parent function

The absolute value parent function is \( y = |x| \). Its minimum value is \( 0 \) (at \( x = 0 \)) because the absolute value of a number is always non - negative, and when \( x = 0 \), \( y=0 \).

Step2: Analyze each option

• Option 1: For the function \( y=x^{2} \), since any real number squared is non - negative (\( x^{2}\geq0 \) for all real \( x \)), and when \( x = 0 \), \( y = 0 \). So the minimum value of \( y=x^{2} \) is \( 0 \).
• Option 2: For the function \( y = x \), this is a linear function with a slope of \( 1 \). As \( x\) approaches negative infinity, \( y\) approaches negative infinity, so it has no minimum value (it can get arbitrarily small).
• Option 3: For the function \( y=-x \), this is a linear function with a slope of \( - 1 \). As \( x\) approaches positive infinity, \( y\) approaches negative infinity, so it has no minimum value (it can get arbitrarily small).
• Option 4: For the function \( y=-x^{2} \), since \( x^{2}\geq0 \), then \( -x^{2}\leq0 \). The maximum value of this function is \( 0 \) (at \( x = 0 \)), and as \( |x|\) increases, \( y\) decreases without bound, so it has no minimum value (it can get arbitrarily small).

Answer:

A. \( y = x^{2} \)