### Home > APCALC > Chapter 7 > Lesson 7.1.4 > Problem7-41

7-41.

Write the equation of the line(s) tangent to $y = x^2 + 2x + 4$ that pass through the origin. .

$y = x^2 + 2x + 4$ has infinitely many tangent lines; two of them go through the origin.

Let the point of tangency be $(a, y(a))$ or $(a, (a^2 +2a + 4))$.

Therefore, the slope of the tangent lines must be $y^\prime(a) = 2a + 2$.
Of course, we do not know the value of '$a$' yet.

Write the equation of the tangent line(s) using Point-Slope form. Then solve for $y$. We will solve for '$a$' next.

Since we know that the lines pass through the origin, evaluate $(x, y)$ for $(0,0)$. This will give you the values of '$a$'.

Use the eTool below to explore the problem.
Click the link at right for the full version of the eTool: Calc 7-41 HW eTool