Answer:
(See explanation and attachment below for further details)
Step-by-step explanation:
The parabola must satisfy the following conditions:
[tex]y + 4 = C\cdot (x - k)^{2}[/tex]
[tex]y + 4 = C\cdot (x^{2}-2\cdot k \cdot x + k^{2})[/tex]
The expression for the x-intercepts are, respectively:
x = -3
[tex]4 = C\cdot [(-3)^{2} - 2\cdot k\cdot (-3)+k^{2}][/tex]
[tex]\frac{4}{C} = 9 + 6\cdot k + k^{2}[/tex]
x = 5
[tex]4 = C\cdot [5^{2}-2\cdot k \cdot (5)+k^{2}][/tex]
[tex]\frac{4}{C} = 25 - 10\cdot k + k^{2}[/tex]
By equalizing both expressions:
[tex]9 + 6\cdot k + k^{2} = 25 - 10\cdot k + k^{2}[/tex]
[tex]16\cdot k = 16[/tex]
[tex]k = 1[/tex]
And,
[tex]C = \frac{4}{25-10\cdot (1)+1^{2}}[/tex]
[tex]C = \frac{1}{4}[/tex]
The equation of parabola is:
[tex]y = \frac{1}{4}\cdot (x-1)^{2} - 4[/tex]
Whose graph is included as attachment.
