Question

Choose the equation below that corresponds to the graph shown.

y = −3x2 − 12x − 14

y = 3x2 + 12x − 14

y = −3x2 + 12x − 14

y = 3x2 − 12x − 14

Answer 1

well, the parabola is going downwards, that means it has a leading negative coefficient, so that rules out 2 options

Answer 2

the coefficient of x^2 is negative so the graph opens downwards so its either a or c

Answer 3

It would be 'c' because negative positive negative!?!

Answer 4

so, notice the vertex of the parabola, it's at (-2, -2)
the parabola equation in vertex form will be => \(\bf y = a(x-h)^2 + k\)
(h, k) = the vertex => (-2 , -2)
so we could rewrite that as \(\bf y = a(x+2)^2 -2\)

so to use a value for "x" and "y", let's pick a point IN THE parabola,, say (-1, -5)
so we can rewrite the vertex form further like \(\bf -5 = a(-1+2)^2 -2\)

that will give us the value for "a" if we solve for "a"
once you know what "a" is, plug it back in \(\bf y = a(x+2)^2 -2\)
and expand to get the equation in standard form

Answer 5

So was I correct?

Answer 6

hmmm to be honest dunno, but if that's what you got as equation