Question

Below is the graph of a parabola with its vertex and another point on the parabola labeled.Write an equation of the parabola.• (-2,3)• (-4,-5)

Answer 1

The equation of the parabola is;

$x\text{ = -}\frac{1}{32}(y-3)^2-2$

Here, we want to write the equation of the parabola

As we can see, for this kind of parabola, the x coordinate becomes the independent variable while the y coordinate becomes the dependent variable

We have the vertex as (-2,3) and the other point as (-4,-5)

We have the general equation form as;

$x\text{ = }a(y-k)^2\text{ + }h$

where (h,k) is the vertex of the parabola

From the given question, h = -2 and k is 3

Susbtituting these values;

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

To get the value of a, we substitute the coordiantes of the other point;

We have this as;

$\begin{gathered} -4=a(-5-3)^2-2 \\ -4=a(-8)^2-2 \\ -4\text{ = 64a-2} \\ 64a\text{ = -4 + 2} \\ a\text{ = }\frac{-2}{64}\text{ =- }\frac{1}{32} \end{gathered}$