### Home > CALC > Chapter 2 > Lesson 2.2.1 > Problem2-53

2-53.

Find the equation of the line through the vertex of $y = 2x^2 + 6x − 20$ with a slope of $- \frac { 7 } { 3 }$. Write your answer in point-slope form.

Find the coordinate of the vertex.

There are many ways to find a vertex. One way is by using the formula:

This will give you the $x$-value of the vertex. Then evaluate $y = 2x^2 + 6x − 20$ to find the $y$-coordinate.

Find the equation of the line in point-slope form.

Since the slope is given and a point is known (the vertex), find the equation of the line in point-slope form: $y − y_1 = m(x − x_1)$