12-10

Warm Up #1: Which graph shows a system of linear equations with no solution? How do you know?

• The first one because it crosses at two points.

• The second one because the line is horizontal.

• The third one because the graphs never cross.

• Infinite

Warm Up #2: Choose the correct order of the vertices below: y = ax² , y = ax²+ c, y = ax² + bx + c

• (0, 0), (0, 0), (0, 0)

• (a, x), (a, c), (b, c)

• (0, 0), (0, c), (-b/2a, y value after plugging in x = -b/2a)

• (a, 0), (0, c), (a, b)

After First Essential Understanding #1: Why does this system have one solution?

• It has a horizontal line.

• The line and curve intersect at one point.

• The quadratic function faces upwards.

• Every math problem has only one solution.

Practice 1:

• (-2, 5)

• (2, 1)

• (0, 1)

• (0, 5)

Practice 2: Solve.

• (0, 4), (-3, -5)

• (3, 4), (-1, 4)

• 9

• (4, 4)

After Problem 2: Why might it have been mathematically easier to subtract the equations with Pool A minus Pool B?

• The negative on the x² would turn to a positive, so we wouldn't have to factor out a negative.

• The smaller numbers would be on bottom.

After GOT IT Problem 2: Why does elimination work well for solving these functions?

• Since both equations equal y, subtracting quickly eliminate the y values.

• Because they are in slope-intercept form.

• Since quadratics have vertices and lines have slopes, they intersect.

• Because I said so.

Practice 3:

• (-1, -7)

• (6, -13), (2, -9)

• (1, -6), (3, -10)

• (1, -8), (2, -9)

Practice 4:

• day -4, -796 players

• day 3, 541 players

• day 13, 2451 players

• The Day After Tomorrow

(skip practice 5) Practice 6: Solve.

• (3, 4), (1, 5)

• (-1, -5), (0, 0)

• (-4, -41), (1/3, 7/3)