Consider the quadratic functions: 𝑓(𝑥) = −2(𝑥 + 3)(𝑥 − 7) and 𝑔(𝑥) = 1/3 (𝑥 + 3)(𝑥 − 7). How are they the same? How are the different? Create another equation that belongs to this family.

Answer 1

The only difference between these quadratic functions are coefficients (-2 and 1/3)

When coefficient is positive (1/3) the functions open upward (like u shape)

When coefficient is negative (-2) the functions open downward (like n shape)

Also regardless sign of the coefficient if the number is greater that function is narrower

so; graph of -2(x+3)(x-7) is narrower (just ignore the sign and think you compare 2 and 1/3)

Hope that helps