Question

PLEASE HELP. 50 POINTS AND BRAINLIEST IF YOU SHOW YOUR WORK

Find equation of parabola with vertex (8,-1) and which passes through point (-5,9)

Answer 1

Answer:

$\displaystyle f(x)=\frac{10}{169}\left(x-8\right)^2-1$

Step-by-step explanation:

We can use the vertex form of a quadratic, which is given by:

$\displaystyle f(x)=a(x-h)^2+k$

Where (h, k) is the vertex.

Since we are given that the vertex is (8, -1), h = 8 and k = -1. Substitute:

$f(x)=a(x-8)^2-1$

Next, we are given that the parabola passes through the point (-5, 9). So, when x = -5, y = 9:

$9=a((-5)-8)^2-1$

Solve for a:

$9=a(-13)^2-1$

So:

$\displaystyle a=\frac{10}{169}$

So, the equation of our parabola is:

$\displaystyle f(x)=\frac{10}{169}\left(x-8\right)^2-1$

Answer 2

Answer:

The equation of our parabola would be:

f(x) = 10/169(x - 8)$^{2}$ - 1