SAT Math Desmos

Equation of a linear function given two points

e.g. The graph of the linear function f contains the points (2, 5) and (4, 11). Which equation defines f?

1. type “table”

2. enter points

3. click “Add Regression” button on the left

Single-variable equations

e.g. How many distinct real solutions does x² - 12x + 27 = 0 have?

Turn it into a system of equations; y = left side of equation and y = right side of equation

Solution to an equation with a constant

1. Turn it into a system of equations; y = left side of equation and y = right side of equation

2. Add slider for k

3. Enter each answer choice

4. Check if each answer choice properly relates x and k

Find the value of a constant in an equation with no real solutions

1. Turn it into a system of equations; y = left side of equation and y = right side of equation

2. Replace constant with each answer choice and check for absence of intersections

Finding the solutions to a given equation in terms of a constant

1. Turn it into a system of equations; y = left side of equation and y = right side of equation

2. Add slider for constant and set it to the given parameters

3. Check intersections

Choosing a point containing a constant that lies on the graph of each equation of a system

e.g. The system of equations below is given:

3x + 2y = 8

9x + 6y = 24

For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system?

1. enter system into Desmos

2. enter each point into Desmos and use the slider to see which point traces the line

The function f(x) is a rational function of the form f(x) = a/(x - b) that passes through the points listed below. What is a + b?

(5,3) (9,1)

1. run a regression with these points

2. click three dots, then “delete regression”

3. type in form of equation (y₁ ~ a/[x₁ - b])

The expression (4x - 29)(15x + 8) is equivalent to the expression ax² + bx + c, where a, b, and c are constants. What is the value of b?

1. Type (4x₁ - 29)(15x₁ + 8) ~ ax₁² + bx₁ + c

2. Type x₁ = [1…5]

b = -403

1. Determine that the x-coordinate of the vertex is -3, since that’s halfway between -9 and 3

2. Write in vertex form: f(x) = a(x + 3)² + k

3. Run a regression between standard and vertex form

4. Type x₁ = [1…5]

5. Add a slider for k for negative values, and see if any answers are true

vertex form

y = a(x - h)² - k

3 indicators of 2 solutions

You take three exams and get scores of 85, 89, and 91. What do you need to get on the fourth exam to get an average of 90?