Question

Willing to brainlist solve 16-17 please during this exam

Answer 1

Answer:

16. B

17. B

Step-by-step explanation:

16. The intercept form of the parabola is

$y=a(x-x_1)(x-x_2),$

where $x_1, x_2$ are two x-intercepts.

In your case,

$x_1=2\\ \\x_2=-8$

so

$y=a(x-2)(x-(-8))\\ \\y=a(x-2)(x+8)$

To find a, substitute coordinates of the point (-6,-4) parabola is passing through

$-4=a(-6-2)(-6+8)\\ \\-4=-16a\\ \\a=\dfrac{1}{4}$

and

$y=\dfrac{1}{4}(x-2)(x+8)$

17. The vertex form of the parabola equation is

$-2p(y-k)=(x-h)^2,$

where (h,k) are the coordinates of the vertex and sign "-" because parabola goes down.

In your case, vertex is (2,3), so

$-2p(y-3)=(x-2)^2$

The vertex is 3 units from the focus, then

$\dfrac{p}{2}=3\\ \\p=6$

The equation of the parabola is

$-2\cdot 6(y-3)=(x-2)^2\\ \\y=-\dfrac{1}{12}(x-3)^2+3$