Question

What is the equation, in standard form, of a parabola that contains the following points?
(–2, –20), (0, –4), (4, –20)

Answer 1

You are given 3 points

Answer 2

The standard form for a parabola
y = ax^2 + bx + c

Answer 3

you need to find a,b, and c

Answer 4

We can use those 3 points, to generate 3 equations with 3 unknowns, a,b,c and solve for those 3 unknowns

Answer 5

Using the first point. (-2, -20)

-20 = a(-2)^2 + b(-2) + c

Answer 6

so we end up with 3 equations like this

-20 = a(-2)^2 + b(-2) + c

-4 = a(0)^2 + b(0) + c

-20 = a(4)^2 + b(4) + c

Answer 7

-20 = 4a - 2b + c

-4 = c

-20 = 16a + 4b + c

Answer 8

so right off the bat you find c = -4

Answer 9

so you are left with

-20 = 4a - 2b - 4
-20 = 16a + 4b - 4

Answer 10

Understand so far?

Answer 11

yeah i do :)

Answer 12

so solving those 2 equations with , a, and ,b...

Answer 13

You will find...a=-2 and b=4

Answer 14

so the parabola containing those 3 given points, in standard form is:

y = ax^2 + bx + c

Answer 15

y = -2x^2 +4x - 4

Answer 16

if you want, you can put in the points and see if the equation holds true , as a extra check

Answer 17

for example the point (-2, -20)

-20 = -2(-2)^2 + 4(-2) - 4 ???

Answer 18

-20 = -8 - 8 - 4 = -20 TRUE

Answer 19

ohhh okay i totally get it now thank you!

Answer 20

no prob, anytime