Question

The vertex of this parabola is at (2,-4). When the y-value is -3, the x-value is

-3. What is the coefficient of the squared term in the parabola's equation?

Answer 1

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (2, - 4), thus

y = a(x - 2)² - 4

To find a substitute (- 3, - 3) into the equation

- 3 = a(- 3 - 2)² - 4

- 3 = 25a - 4 ( add 4 to both sides )

1 = 25a ( divide both sides by 25 ), hence

a =
`(1)/(25)`

y =
`(1)/(25)` (x - 2)² - 4 ← in vertex form

=
`(1)/(25)` (x² - 4x + 4) - 4 ← in expanded form

Hence the coefficient of the x² term is
`(1)/(25)`

Answer 2

Answer:-5

Explanation: