Question

High lvl math: Find the parabola y=ax^2+bx+c which intersects the x-axis at the points x=3 and x=-5, and the y-axis at the point y=30

Answer 1

determine the general solution with those roots:

(x-r1)(x-r2) = x^2-(r1+r2)x + r1r2

Answer 2

when x=0, we have y = r1r2 which needs to be scaled to equal 30

Answer 3

You have c=30, now use your x values to get simultaneous equations in a and b.

Answer 4

x^2-(r1+r2)x + r1r2 ; using r1= 3 and r2 = -5

x^2 -(3--5)x + (3*-5)

x^2 -8x -15 ; at x=0; y=-15 ; -15s = 30 when s=-2

y = -2(x^2 -8x -15)

Answer 5

hmm, im off a bit

Answer 6

i got me roots off somehow :) let me dbl chk

Answer 7

I get (-2x-10)(x-3) which can be arranged a bit, obviously.

Answer 8

-2(x-3)(x+5)

Answer 9

I prefer your method myself but the simul eqs might be a bit easier to understand.

Answer 10

thanks for help :)

Answer 11

x^2 -(3--5)x + (3*-5)
^
thats spose to be a +- :)

Answer 12

ur welcome.

Answer 13

estudier can you show me your work if you have time because I got something wrong