Question

algebra 2a semester online practice
complete this assessment to review what youve learned. it will not count toward
what is the point of inflection of the function $y = -3(x - 9)^3 + 10$? (1 point)
$\circ$ $(9, 10)$
$\circ$ $(9, -10)$
$\circ$ $(-9, 10)$
$\circ$ $(-9, -10)$

Explanation:

Step1: Recall Inflection Point of Cubic Function

For a cubic function in the form \( y = a(x - h)^3 + k \), the point of inflection is at \( (h, k) \). This is because the graph of \( y = (x - h)^3 + k \) is a transformation of the basic cubic function \( y = x^3 \), which has an inflection point at the origin \((0,0)\). Shifting horizontally by \( h \) and vertically by \( k \) moves the inflection point to \((h, k)\).

Step2: Identify \( h \) and \( k \) in Given Function

The given function is \( y = -3(x - 9)^3 + 10 \). Comparing with \( y = a(x - h)^3 + k \), we have \( h = 9 \) and \( k = 10 \).

Step3: Determine Inflection Point

Using the formula for the inflection point of a cubic function, the inflection point is \( (h, k)=(9, 10) \).

Answer:

A. \((9, 10)\)