Question

Which of the following is the equation of the parabola having vertex (-2,4) and passing through the point (1,1)?

Answer 1

Standard form:\[ y = a(x - h)^2 + k\]
Where \((h, k)\) is the vertex.

Answer 2

@Operand what is a?

Answer 3

So would that make it y=-(x+2)^2+4

Answer 4

You solve for \(a\) by plugging in \((x, y)\), in your case, x is 1, and y is 1.

Answer 5

So plugging in what we know: \[1 = a(1 - (-2))^2 + 4\]
Solve for \(a\).

Answer 6

a=1?

Answer 7

Nope.

Hint: \(a\) is a fraction.

Answer 8

-1/3

Answer 9

Correct.

Answer 10

You now know your answer. Just input, the vertex, and \(a\) into the standard form.

Answer 11

Oh ok so the answer would be y=-1/3(x+2)^2+4

Thank you for your help :)

Answer 12

You are welcome.