Question

Graph a parabola whose x-intercepts are at x = -3 and x = 5 and whose minimum value is y = -4.

Answer 1

here iz da answer

Explanation:

Answer 2

(See explanation and attachment below for further details)

Explanation:

The parabola must satisfy the following conditions:

`y + 4 = C\cdot (x - k)^(2)`

`y + 4 = C\cdot (x^(2)-2\cdot k \cdot x + k^(2))`

The expression for the x-intercepts are, respectively:

x = -3

`4 = C\cdot [(-3)^(2) - 2\cdot k\cdot (-3)+k^(2)]`

`(4)/(C) = 9 + 6\cdot k + k^(2)`

x = 5

`4 = C\cdot [5^(2)-2\cdot k \cdot (5)+k^(2)]`

`(4)/(C) = 25 - 10\cdot k + k^(2)`

By equalizing both expressions:

`9 + 6\cdot k + k^(2) = 25 - 10\cdot k + k^(2)`

`16\cdot k = 16`

`k = 1`

And,

`C = (4)/(25-10\cdot (1)+1^(2))`

`C = (1)/(4)`

The equation of parabola is:

`y = (1)/(4)\cdot (x-1)^(2) - 4`

Whose graph is included as attachment.