Question

how would the graph of $y = 3x^2 + 2x + 1$ change if the equation was altered to $y = -3x^2 + 2x + 1$?

a. the parabola would widen
b. the parabola would shift upward
c. the parabola would open downward
d. the parabola’s vertex would move to the right

Explanation:

Step1: Analyze coefficient of $x^2$

Original: $y=3x^2+2x+1$, coefficient $a=3$
New: $y=-3x^2+2x+1$, coefficient $a=-3$

Step2: Interpret coefficient changes

The sign of $a$ flips from positive to negative. For parabolas $y=ax^2+bx+c$, positive $a$ opens upward, negative $a$ opens downward. The magnitude of $a$ is unchanged, so width stays the same. Linear and constant terms are unchanged, so vertex horizontal/vertical position does not shift.

Answer:

c. The parabola would open downward