# Thread: Two really easy graph problems

1. ## Two really easy graph problems

I seem to be missing something really easy step or something.

On a separate piece of paper, sketch the graph of the parabola . On the same graph, plot the point . Note that there are two tangent lines of that pass through the point .
Specifically, the tangent line of the parabola at the point passes through the point where . The other tangent line that passes through the point occurs at the point .

Find the number a=

Thanks!

2. Here is what we know.

The slope between two points is given by

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

also the slope at a point is the derivative evaluated at that point.

Using the above we get and the points $\displaystyle (a,a^2+4);(0,-2)$

$\displaystyle m=\frac{a^2+4-(-2)}{a-0}=\frac{a^2+6}{a}$

the derivative at that point is

$\displaystyle y'=2x \implies m=2a$

Now set them equal and solve for a

$\displaystyle 2a=\frac{a^2+6}{a}$