Question

what feature of the parabola is directly affected by both coefficients a and b in the equation $y = ax^2 + bx + c$?
a. the y - intercept
b. the width
c. the x - intercepts
d. the vertex

Explanation:

• The y-intercept is found by setting $x=0$, giving $y=c$, so it only depends on $c$.
• The width of the parabola is determined solely by $|a|$, with larger $|a|$ making it narrower.
• The x-intercepts are found by solving $ax^2+bx+c=0$, but while $a$ and $b$ are involved, the vertex's x-coordinate is $-\frac{b}{2a}$, which directly relies on both $a$ and $b$ to determine the horizontal position of the vertex (a key feature of the parabola).

Answer:

d. The vertex