? is y=a(x−h)^2 +k where (h, k) represents the coordinates of a specific location on the graph (included in the term)

Answer 1

Yes, the equation \( y = a(x - h)^2 + k \) represents a parabola in vertex form. In this equation:

• \( (h, k) \) is the vertex of the parabola. This is the point where the parabola changes direction, and it represents the highest or lowest point of the graph depending on the value of \( a \).
• The parameter \( a \) determines the width and direction of the parabola:
  • If \( a > 0 \), the parabola opens upwards.
  • If \( a < 0 \), the parabola opens downwards.
  • The larger the absolute value of \( a \), the "narrower" the parabola, while a smaller absolute value of \( a \) makes it "wider".

In summary, \( (h, k) \) is indeed the specific location of the vertex on the graph of the parabola defined by the equation.