What is the standard form of the equation of the parabola shown in the graph?

Question

asked Jan 3, 2019 227k views

2 Answers

FryHard · Answer 1 · 2019-01-09T00:01:37+0000

Answer:

Explanation:

Since, the standard form of a parabola which is along to the y-axis,

y=a(x-h)^2+k^2

Where (h,k) is the vertex of the parabola,

By the given diagram,

The vertex of the parabola along to the y-axis = (0,0)

⇒ h = 0, k=0

By substituting these values in the above equation,

We get,

y=a(x-0)^2+0

$\implies y = ax^2$ --------(1)

Now, again by the given diagram the parabola is passing through the point (-4,-1),

⇒ This point will be satisfy the equation of parabola,

⇒
-1 = a(-4)^2

⇒
-1 = 16a

⇒
(-1)/(16)=a

By substituting this value in equation (1),

We get,

y=(-1)/(16)x^2

$\implies -16 y = x^2$

Which is the required equation of the given parabola.

⇒ First option is correct.