Question

What is the equation of a parabola y(x) that has a vertex at point (− 1/3 , 0.3) and passes through point (− 2/15 , − 1/2 ).

Answer 1

Answer:

$y=-20(x+\frac{1}{3})^2+0.3$

Step-by-step explanation:

The vertex form of a parabola is given by

$y=a(x-h)^2+k$

Here (h,k) is the vertex.

We have been given that vertex is at  (− 1/3 , 0.3) . Thus, the vertex form of the parabola is

$y=a(x+\frac{1}{3})^2+0.3$

Now, it passes through point (− 2/15 , − 1/2 ). Thus, we have

$-\frac{1}{2}=a(-\frac{2}{15}+\frac{1}{3})^2+0.3\\\\\frac{1}{25}a+0.3=-\frac{1}{2}\\\\\frac{1}{25}a+0.3-0.3=-\frac{1}{2}-0.3\\\\\frac{1}{25}a=-0.8\\\\a=-20$

Therefore, equation of parabola is given by

$y=-20(x+\frac{1}{3})^2+0.3$