Question

Question 4 (Multiple Choice Worth 1 points)

Choose the equation below that corresponds to the graph shown.

graph of a u-shaped figure opening downward with a maximum point of (−2, −2)

y = −3x2 − 12x − 14

y = 3x2 + 12x − 14

y = −3x2 + 12x − 14

y = 3x2 − 12x − 14

Answer 1

you know you can add a picture here by using the [Attach File] blue button

Answer 2

the vertex form of a parabola equation will be \(\bf y = a(x - h)^2 + k\)
where the vertex of it is at (h , k) coordinates
notice yours

the vertex of it is at (-2, -2) that means (h, k) that means
\(\bf y = a(x - h)^2 + k \implies y = a(x + 2)^2 -2\)

so what's "a", well, we dunno
but we can see another point it passes through, say (-1, -5)
so we can say, that when x = -1, y = -5
so \(\bf y = a(x - h)^2 + k \implies y = a(x + 2)^2 -2\\
(-1, -5)\\
y = a(x + 2)^2 -2 \implies (-1) = a((-5) + 2)^2 -2\\ \implies -1 = a9-2 \implies 1 = 9a \implies \cfrac{1}{9} = a\)

Answer 3

since the parabola is going downwards, so the "a" is negative, that is \(-\cfrac{1}{9} \)

Answer 4

oh ok

Answer 5

so, \(\bf y = a(x - h)^2 + k \implies y = a(x + 2)^2 -2\\
\implies y = -\cfrac{1}{9}(x + 2)^2 -2\)

and we could expand that, to see what we get, for the "standard form"

Answer 6

so..... see if you can expand it... and match it with one of your choices :)

Answer 7

will it be this one y = 3x2 − 12x − 14

Answer 8

dunno, you'd need to expand it to get the standard form

Answer 9

I don't know that

Answer 10

http://www.statisticslectures.com/images/trinomial11.gif <--- to expand the binomial

Answer 11

ok but i don't know how to do that

Answer 12

well.... if you were given the exercise, there seems to be an assumption that you're supposed to know how to, otherwise giving you the exercise would be improper