I am trying to study for the SAT math but I am taking it though Duke Tip, so I barley understand parabolas. (Ugh)
When the parabolas are in the form y=ax2+bx+c, I think c is the y intercept, and a determines whether it opens up or down. but I don’t understand what b is!?
Plus is there any other stuff I should know about parabolas?
Thanks! Please help:))))))))
@kendylc Yup. If x = 0, then y = c, so (0,c) is the y-intercept. If a > 0, then the parabola opens up, i.e. it has a minimum value.
Even as a math major, it might be tricky for me to really explain the significance of the x coefficient (what it really represents). Maybe someone else has a better explanation.
Any parabola of the form y = ax^2 + bx + c attains its minimal (or maximal) value at x = -b/2a. So for some fixed a, the value of b determines the parabola’s axis of symmetry.
Also, the sum of the two roots of the polynomial y = ax^2 + bx + c is -b/a (regardless of whether the roots are real or not). This can be seen from factoring ax^2 + bx + c as a(x - r1)(x - r2). A similar rule follows for sum/product of roots of higher degree polynomials.
So if b=0, the parabola is symmetric about the y-axis.
If b=/=0, the parabola is shifted to the right or left (depending on the sign of b/a) of the y-axis
just like c shifts the parabola up or down depending on its sign.
A parabola can be rewritten as
y - y1 = a (x - x1)^2
@payn4ward Sort of – but if b changes while a and c remain constant, it’s not a simple translation in the +x or -x direction.
yes, I just meant the difference between whether b=0 or not zero.
thank you so much! That really helps a lot:) @MITer94