Question

how do i find the equation of a parabola give x-intercepts and another point

Answer 1

You can "convert" x intercepts to factors. When you FOIL everything, you can then plug in the additional point to find the value of 'a' in y=ax^2 +bx+c and you have the equation :)

Answer 2

an example would be nice to work with

Answer 3

@satellite73 because i'm asked to find the equation of a parabola given the x-intercepts -4 and 3 and that passes through (2,7)

Answer 4

So then you have factors of (x+4) and (x-3)

multiplied out, they get x^2 +x-12

Then plug into y=ax^2 +bx +c
to get 7=a(2)^2 + 2 -12
then a = -7/40

so the equation is y=(-7/40)x^2 +x -12 ... I think XD

Answer 5

start with
\[y=a(x+4)(x-3)\]and multiply out

Answer 6

you get
\[y=a(x^2+x-12)\] and now you need to solve for "a" but you know that if you replace x by 2 you get y =7 so write
\[7=a(2^2+2-12)\]
\[7=a(-6)\]
\[a=-\frac{7}{6}\]

Answer 7

so then the equation for the parabola would be f(x) = -7/6 (x+4)(x-3)

Answer 8

and therefore your answer is
\[y=-\frac{7}{6}(x^2+x-12)\]which you can multiply out of you like

Answer 9

yes

Answer 10

@wombat @satellite73 thank you so much for the help