After you set the two expressions for $y$ equal, rearrange the equation so that it looks like $ax^2 + bx + c = 0$. What are $a$, $b$, and $c$ in your new equation?

For a quadratic $ax^2 + bx + c = 0$, there is a direct formula for the sum of the solutions in terms of $a$ and $b$. Recall that formula so you can find the sum without solving for each solution individually.

In the first expression line, type y = x^2 - 5x + 6 to graph the parabola.

In the second expression line, type y = 2x - 2 to graph the line on the same axes.

Click on each point where the line and the parabola intersect; Desmos will display their coordinates $(x_1, y_1)$ and $(x_2, y_2)$. Note the two $x$-values.

In a new expression line, type the sum of the two $x$-values you observed (for example, if the $x$-values were $a$ and $b$, type a + b with the actual numbers). The resulting value is the sum of the $x$-coordinates of the intersection points.

The points of intersection have the same $x$- and $y$-values in both equations, so set the right sides equal:

Move all terms to one side to get a quadratic equation:

The solutions to this quadratic are the $x$-coordinates of the intersection points.

Write the quadratic in standard form $ax^2 + bx + c = 0$.

Here, compared to $ax^2 + bx + c = 0$:

• $a = 1$
• $b = -7$
• $c = 8$

These coefficients will help you find the sum of the solutions without solving the quadratic completely.

For any quadratic equation $ax^2 + bx + c = 0$ with solutions (roots) $r_1$ and $r_2$:

• The sum of the solutions is

This is known as Vieta's formula. In this problem, $r_1$ and $r_2$ are the $x$-coordinates of the intersection points.

Use $a = 1$ and $b = -7$ in the formula $r_1 + r_2 = -\dfrac{b}{a}$:

So, the sum of the $x$-coordinates of the points of intersection is $7$, which corresponds to choice C.