Question

Which of the following is the correct equation for this function?
it shows a graph with a parabola facing upwards with a vertex of (-3,-2) and the x intercept of (-2,0) and (-4,0)


A. y=x^2+3x-2
B. y=2=-2(x+3)^2
C. y=(x+4)(x+2)
D. y+2=2(x+3)^2

Answer 1

option B looks invalid - can you check it please?

Answer 2

ph my bad its supposed to be y+2=-2(x+3)^2

Answer 3

D

Answer 4

thanks just wondering how did you get that answer so i know how to do it in future

Answer 5

Substitute x = -2 in to the equation and you get y = 0.
Substitute x = -4 in to the equation and you get y = 0

So it has x intercept of (-2,0) and (-4,0)

Answer 6

But this is not the only one of the options for which this is true

so we need to check the vertex as well

Answer 7

so you need to simplify the function, expanding out the brackets, and get it in the form of y = ......
which is
y= 2x^2+12x+16

Answer 8

differentiate this to get

dy/dx = 4x + 12

At the vertex, dy/dx = 0

so

4x + 12 = 0

so 4x = -12

so x = -3

Answer 9

Sub this in to y= 2x^2+12x+16

to get y = -2

so the vertex is -3, -2)

D fulfils all conditions specified

so its the answer!

Answer 10

cool thanks alot! :)

Answer 11

you are most welcome :-)

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