Question

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

Answer 1

Answer:

(See explanation and attachment below for further details)

Step-by-step 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

$4 = C\cdot [(-3)^{2} - 2\cdot k\cdot (-3)+k^{2}]$

$\frac{4}{C} = 9 + 6\cdot k + k^{2}$

x = 5

$4 = C\cdot [5^{2}-2\cdot k \cdot (5)+k^{2}]$

$\frac{4}{C} = 25 - 10\cdot k + k^{2}$

By equalizing both expressions:

$9 + 6\cdot k + k^{2} = 25 - 10\cdot k + k^{2}$

$16\cdot k = 16$

$k = 1$

And,

$C = \frac{4}{25-10\cdot (1)+1^{2}}$

$C = \frac{1}{4}$

The equation of parabola is:

$y = \frac{1}{4}\cdot (x-1)^{2} - 4$

Whose graph is included as attachment.